Development of surface reconstruction algorithms for optical interferometric measurement

Dongxu WU, Fengzhou FANG

Front. Mech. Eng. ›› 2021, Vol. 16 ›› Issue (1) : 1-31.

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Front. Mech. Eng. ›› 2021, Vol. 16 ›› Issue (1) : 1-31. DOI: 10.1007/s11465-020-0602-6
REVIEW ARTICLE
Mechanisms and Robotics - REVIEW ARTICLE

Development of surface reconstruction algorithms for optical interferometric measurement

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Abstract

Optical interferometry is a powerful tool for measuring and characterizing areal surface topography in precision manufacturing. A variety of instruments based on optical interferometry have been developed to meet the measurement needs in various applications, but the existing techniques are simply not enough to meet the ever-increasing requirements in terms of accuracy, speed, robustness, and dynamic range, especially in on-line or on-machine conditions. This paper provides an in-depth perspective of surface topography reconstruction for optical interferometric measurements. Principles, configurations, and applications of typical optical interferometers with different capabilities and limitations are presented. Theoretical background and recent advances of fringe analysis algorithms, including coherence peak sensing and phase-shifting algorithm, are summarized. The new developments in measurement accuracy and repeatability, noise resistance, self-calibration ability, and computational efficiency are discussed. This paper also presents the new challenges that optical interferometry techniques are facing in surface topography measurement. To address these challenges, advanced techniques in image stitching, on-machine measurement, intelligent sampling, parallel computing, and deep learning are explored to improve the functional performance of optical interferometry in future manufacturing metrology.

Keywords

surface topography / measurement / optical interferometry / coherence envelope / phase-shifting algorithm

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Dongxu WU, Fengzhou FANG. Development of surface reconstruction algorithms for optical interferometric measurement. Front. Mech. Eng., 2021, 16(1): 1‒31 https://doi.org/10.1007/s11465-020-0602-6

1 1 Introduction

Multifingered robotic hands have been used for grasping and manipulating tools in the early stages of robotic research to achieve precise manipulation of targets through finger movements [1], such as Stanford/JPL hand [2], Utah/MIT hand [3], NASA hand [4], DLR hands [5], and DLR-HIT hands [6]. However, the design of these dexterous hands is mainly aimed at grasping or operating objects in static or quasi-static state. It focuses on achieving bionic movement functions on mechanical devices. In fact, physical collisions are unavoidable when multifingered hands are exposed to unstructured environments, and the energy generated by impacts and vibrations can damage the hardware system of multifingered hands. Although compliance control can submit a multifingered hand to disturbances, it cannot withstand high-frequency external impacts due to delays associated with sensing, control, and communication [7,8]. Hence, the movements of the hand require rigorous planning and operation on account of the fragile hardware of the fingers, thereby hindering the application of many manipulation strategies, such as grasping in environments where obstacles move quickly and interacting with humans or other robots. Human hands have certain impact resistance in the interaction process because of flexibility of tendons, joints, and muscles; they can repair injury caused by external impact energy because of the self-repairing ability of bio-tissues. As proposed in Refs. [9,10], the hardware system of multifingered hand is protected by absorbing impact energy through elastic materials, such as joints or fingers made of elastic materials, to achieve mechanical robustness. Although this scheme achieves passive compliance, it cannot satisfy high precision or strength manipulation requirements. A method of reducing system bandwidth by connecting an elastic element in series between link side and actuator is proposed to passively comply with the mechanical system and achieve safety and accuracy. In this method, the environmental impact energy from the link side is stored by the elastic element and released slowly to protect the actuator and other components from damage, thereby achieving high mechanical robustness. Nevertheless, the actuators proposed in Refs. [1114] are extremely large to be integrated into a compact robotic hand. Hence, Grebenstein et al. [15] proposed a compact, lightweight, tendon-driven mechanism based variable stiffness actuator (VSA) for robot hands and integrated it in the DLR hand arm system; as a result, the hand can withstand the impact of high speed. However, the mechanical system is complex and costly to manufacture and maintain. Ishikawa team [16] proposed a compact-size actuator called “MagLinkage” that applies magnetic coupler instead of rigid coupler in joint drive system and a three-fingered hand. The magnetic coupling of the MagLinkage is destructible without any structural damage under overload to protect the hand from damage. This hand can only grasp small objects due to the limited force capacity of the magnetic couplers. Based on the analysis of the properties (fingertip force, weight, accuracy, fabrication, and cost) of prevalent dexterous hands and the principle of passive compliance of mechanical system illustrated in Tab.1 [1726], this study proposes an antagonistic variable stiffness dexterous finger (AVS-finger) mechanism. Compared with the prevalent dexterous hand, the main goal is to use universal gears, motors, and more reliable mechanisms to achieve robustness of the dexterous hand against physical impacts. Therefore, the AVS-finger based on gear transmission tends to be more reliable and easier to manufacture and maintain than cable-driven dexterous hands. In addition, the finger has the following characteristics: Adjust its mechanical stiffness according to different task requirements and enhance the dynamic performance of finger movement by storing energy.
Tab.1 Overview of prevalent dexterous hands
Hands Force/N Driven mechanism Actuator Numbers of
Fingers Finger joints DOFs Actuators
Utah/MIT hand Tendon Cylinder 4 16 16 32
Stanford/JPL hand Tendon Motor 3 9 9 12
DLR hand II 30 Gear, tendon Motor 4 16 12 12
Shadow hand [17] Tendon Pneumatic muscle 5 22 18 36
Gifu hand III [18] 2.8 Gear, linkage Motor 5 20 16 16
DLR/HIT hand II 10 Gear, tendon Motor 5 20 15 15
UB hand IV [19] Tendon Motor 5 20 20 25
DEXHAND [20] 25 Tendon Motor 4 16 12 12
Awiwi hand [21] 20–30 Tendon Motor 5 21 20 39
R2 hand 22.5 Tendon, linkage Motor 5 18 12 16
Sandia hand [22] 10 Tendon Motor 4 12 12 12
SVH hand [23] Gear, linkage Motor 5 20 20 9
CEA hand [24] 4.2 Tendon, linkage Motor 5 22 18 18
MagLinkage hand 6.2 Magnetic gear, gear Motor 3 8 8 8
THU hand [25] Tendon Motor 5 16 12 12
FLLEX hand [26] 40 Tendon Motor 5 20 12 12
This paper is organized as follows. In Section 2, the implementation of the VSA principle in the finger mechanism is elaborated. Section 3 carries out statics, mechanical stiffness, and energy modeling and derives the finger stiffness adjusting strategies. In Section 4, experiments are conducted to validate the manipulating, grasping, force, and robustness performance of the finger, identify the finger joint stiffness characteristics, and illustrate the results of the finger stiffness variation operation. Finally, conclusions with future work are summarized in Section 5.

2 2 Mechanical design of the finger based on VSA principle

Dexterous hands require not only anthropopathic grasping and manipulation characteristics, but also compliance to unpredictable physical impacts to guarantee their safety. The anti-impact ability of its finger, as the direct transmitter of movements and forces between the dexterous hand and the object, is very important to improve the overall mechanical robustness of the hand. VSA principle has been widely implemented in various interactive robots. However, due to the addition of extra actuators, greatly increasing the weight, volume, and complexity of the system is unavoidable. This condition is not conducive to the implementation of VSA principle in dexterous hands with very strict weight and volume requirements. The design of the VSA-based finger mechanism is elaborate in this section. A differential mechanism is adopted in the connection between the finger links and the two actuation units to enable the two actuators to form antagonism in variable stiffness joint (VSJ) mode or form collaboration in series elastic joint (SEJ) mode. Moreover, fingers are more energy-efficient than conventional antagonistic VSAs.

2.1 2.1 VSA principle

Passive compliance of mechanical systems can be implemented by damping or elastic mechanisms. Compliance through elastic mechanisms is a reliable and widely used method of compliance for mechanical systems. Typical forms are the series elastic actuator (SEA) and the VSA, and the VSA principle is introduced as follows.
Compared with SEA, VSA can actively adjust mechanical stiffness and potential energy to satisfy various task requirements. For a decelerated flexible mechanical system, the part between the actuation side and the load side can be regarded as a coupling block to transmit forces and movements, as shown in Fig.1. When a generalized force F(φ) is exerted to the actuation frame, a generalized actuation frame deflection x and a generalized load frame deflection q are obtained until F(φ) is balanced with the generalized force Fext at the load frame. The transmission stiffness kT of the coupling block is defined by
Fig.1 Schematic of a flexible mechanical system.

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kT(φ)=F(φ)φ,
where φ is the compliant deflection, and φ = xq. The actuation source and the coupling block constitute a flexible mechanical system, and its stiffness ksys is defined by
ksys(φ)=F(φ)q=Fextq.
Fig.2 depicts two main configurations of VSA: antagonism and series. The series-VSA uses an active nonlinear elastic mechanism to connect actuator 1 with the load side. The driving force is generated by actuator 1, and the secondary actuator 2 adjusts the stiffness of the nonlinear elastic mechanism by adjusting the lever arm or preloading the nonlinear spring mechanisms [2733] (as shown in Fig.2(a)). The disadvantage of this method is that actuator 2 does not participate in the torque output of VSA with more additional weight and size, and the energy utilization rate is low. In the antagonistic-VSA (as shown in Fig.2(b)), the load is connected with two actuators through two nonlinear elastic mechanisms [34,35]. The two actuators exert preload on the elastic elements in advance to change the balance state of the two nonlinear elastic mechanisms, leading to the ability of active joint stiffness variation. The disadvantage of this method is that two actuators are used to drive one-degree of freedom (1-DOF), which increases the complexity of the system. For example, in the DLR hand arm system [36], only a 19-DOF hand is driven by 38 actuators, greatly increasing the cost and complexity of the system.
Fig.2 Two configurations of VSA. (a) Series VSA, (b) antagonism VSA.

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The stiffness of human body joints is regulated differently to different types of operations, as illustrated in Fig.3. Case 1 in Fig.3(a): Stirring a cup of liquid with a finger by the motion of the metacarpophalangeal (MCP) joint while the distal interphalangeal (DIP) and proximal interphalangeal (PIP) joints of the finger are completely abducted. Case 2 in Fig.3(b): Punching with elbow joint locked at 90° to increase arm stiffness, and the fist is driven by the movement of the shoulder to increase the power of the strike. Case 3 in Fig.3(c): Most finger joints are adducted and locked to increase the stiffness of fingers and cope with the large friction resistance at the beginning of screwing to tighten a bottle cap. Case 4 in Fig.3(d): More finger joints are abducted as the cap becomes looser. Case 5 in Fig.3(e): A finger fillips a ball on the horizontal workbench without energy storage. Case 6 in Fig.3(f): A finger fillips the same ball on the horizontal workbench with energy storage. In case 1, the finger requires higher joint stiffness to improve the system bandwidth to increase the motion following the fingertip ability. Comparing cases 2, 3, and 4, the human body requires higher joint stiffness to improve the force gain of the end effector in cases 2 and 3, whereas the human body loosens the muscles to reduce the joint stiffness in case 4, thereby reducing energy consumption and muscle and joint injury. Comparing cases 5 and 6, energy storage in the muscles greatly increases the speed and power of the finger movement. These cases indicate that a human will increase body stiffness at the expense of a part of the joint mobilities when performing heavy or precise manipulations and decrease body stiffness to increase the joint mobilities when performing light or imprecise manipulations. Moreover, the energy storage capacity of muscles is very excellent and effective in enhancing the dynamic performance of the body.
Fig.3 Active human body stiffness variations in different manipulations. (a) Finger stirring with DIP joint and PIP joint fully abducted to achieve higher finger stiffness, (b) punching with elbow joint locked at 90° to increase arm stiffness, (c) finger stiffness is increased by adducting finger joints to resist static friction in the tight phase of cap screwing, (d) more finger joints are abducted, and their stiffness decrease in the loose phase of cap screwing, (e) filliping without energy storage, and (f) filliping with energy storage.

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2.2 2.2 Mechanical implementation of VSA principle in the finger system

The finger is required to be sufficiently robust against physical impacts, compact, light-weight, and easily manufactured and maintained. More detailed indicators are shown in Tab.2, and the detailed mechanical implementation of the finger is elaborated.
Tab.2 Primary physical design goals of the mechanical finger
Design values Criteria
Fingertip force The finger should be sufficiently strong; the maximum fingertip force is not less than 30 N
Compliant deflection range The maximum compliant deflection angle of each finger joint is not less than 20°
Weight and volume The finger mechatronic system should be highly integrated to accommodate the compact size of the dexterous hand
Number of actuators The ratio of the number of actuators to the DOFs of the actuated joint is not more than 2
Finger kinematics configuration The finger kinematics configuration can achieve dexterous manipulation ability of the hand
The original motivation of VSA principle is to ensure the safety of the mechanical system. Therefore, a compromise method is implemented by sacrificing a part of the finger DOFs to adjust the finger joint stiffness. This method not only enables the finger to actively adjust its joint stiffness and potential energy, but also avoids the disadvantage of the large size of VSAs. Based on the principle of mechanical passive compliance, a two-joint (J1 and J2) antagonistic variable stiffness dexterous finger is developed, as shown in Fig.4. For ease of manufacture and assembly, the finger mechanism is designed in three modules: two compliance actuation unit (CAU) mechanisms and a finger joint differential mechanism. The finger joint differential mechanism consists of an input gear 1, an input gear 2, an output gear, and the proximal phalanx, as shown in Fig.4(a). The driving forces of the two CAUs are transferred from the synchronous belt to the two input gears. Input gear 1 and input gear 2 are used as two sun wheels, the output gear as planetary wheel, and the proximal phalanx as planetary frame, forming a differential mechanism. Moreover, the rotation of the output gear drives the distal phalanx. This variable stiffness method integrates VSAs excellently into the robot finger and reduces the number of actuators, thereby avoiding the disadvantages of VSAs, such as large size and system complexity, and increases the system reliability.
Fig.4 Mechanical system of the AVS finger. (a) Sectional view of the finger CAD model, and (b) sketch of the finger mechanism.

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CAU is mainly composed of motor, circular spline (CS), flexspline (FS), wave generator (WG), and nonlinear elastic mechanism, as shown in Fig.5. When the FS is subjected to external load, the slider prevents the rigid wheel from deflecting until the torque synthesized by spring forces and the CS torque are in equilibrium. The relationship between CS torque and CS deflection is nonlinear because the force action point moves on the lever. The nonlinear elastic mechanism plays two main roles in CAU: storing kinetic energy as potential energy and acting as flexible connection between actuator and base to bear external load directly. Only the stiffness of the nonlinear elastic mechanism is variable that is related to the deformation of the elastic element and can be varied by changing the precompression of the elastic element, whereas the stiffness of the linear elastic mechanism is immutable. The combination of linear springs and nonlinear mechanism can be used to obtain nonlinear elastic mechanism stiffness.
Fig.5 Sectional view of CAU.

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The finger joint differential mechanism not only achieves the difference between the 2-DOF rotations of the two finger joints with parallel axes, but also enables the finger joint stiffness to be variable by loading each other between two CAUs without any additional actuators. Fig.6(a) depicts the SEJ mode: CAUs operate as nonlinear SEAs and collaborate with each other to drive finger joints when both phalanxes are not obstructed. The torques of the two CAUs flow through the finger joint differential mechanism to the two finger joints, and the differential between CAU1 and CAU2 drives the movement of J1 and J2. Fig.6(b) depicts the VSJ mode: The finger operates on the principle of VSA when J1 or J2 is obstructed by internal mechanical limitations or objects grasping at motionless state. The torque applied by CAU2 to the input gear 2 is delivered through the output gear to the input gear 1 and eventually becomes an additional load to CAU1, causing CAU1 and CAU2 to be pre-compressed and vice versa. The pre-compression of the two CAUs’ nonlinear elastic mechanisms is controllable and ultimately synthesizes the ability of the finger joint stiffness to vary.
Fig.6 Finger operating mode switches between SEJ and VSJ modes. (a) SEJ mode and (b) VSJ mode.

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3 3 Finger mathematical modeling

In this section, the kinematics, joint stiffness, and potential energy of the finger are derived and are finally used as the basis for finger stiffness variation.
Passive compliance by appending elastic elements to mechanical systems can excellently solve collision problems. However, it can also cause inaccuracies and delays in the finger system. An accurate model of finger should be built to accurately control finger movement. Building this model is very difficult because of the flexibility of synchronous belt and shaft parts. By comparison, the springs are much softer than other parts in the finger mechanism. Therefore, spring-dominated compliance should be considered primarily. The moment of the finger joint is synthesized by the moment of two CAUs. Different CAU stiffness and finger joint stiffness are responded when the finger is subjected to different external forces due to the nonlinearity of CAU stiffness. In this section, the mathematical model between the external loads of the upper finger and the CAU torques is described by establishing the Jacobian of the finger, and then the corresponding stiffness of the finger joint is solved, thereby providing the basis for the finger operating strategy.

3.1 3.1 Kinematics and dynamics

Fig.7 depicts the Denavit–Hartenberg model and the two CAU kinematics models.
Fig.7 Kinematics models of finger links and CAUs.

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The equation for converting CAU output axis rotations to finger joint abduction/adduction angles is as follows:
[θ1θ2]=TK[q1q2],
where θ1 and θ2 are the angular positions of J1 abduction/adduction and J2 abduction/adduction, respectively, q1 and q2 are the angular positions of CAU1 output shaft and CAU2 output shaft, respectively, and TK is the transformation matrix of forward joint kinematics and non-singular. TK = [12pa12pa;12papb12papb], where pa and pb are the transmission ratios of synchronous belt and differential gear, respectively.
The equation for converting CAU output torques to finger joint torques is as follows:
[τ1τ2]=TD[τCAU1τCAU2],
where τ1 and τ2 are J1 torque and J2 torque, respectively, TD=(TK1)T, and TD is the transformation matrix of forward joint dynamics and non-singular.

3.2 3.2 Finger joint stiffness modeling

In this section, the finger joint stiffness model is established. Fig.8 depicts the circular spline of the ith (i = 1,2) CAU in the deflected position. In the ith (i = 1,2) CAU, an external load exerted on the finger causes such equilibrium as
Fig.8 Circular spline in deflected position.

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{Fsi=(F0i+KsΔxsi)(F0iKsΔxsi)=2KsΔxsi,τCSi= 2KsR2tanθCSi,
where Fsi, F0i, ∆xsi, Ks, θCSi, τCSi, and R are the resultant spring force on the slider, the initial spring force, the deflection of the slider, the stiffness of linear spring, the angular displacement of CS, CS torque, and the distance between the CS axis and the slider routine, respectively.
In Eq. (5), ∆xsi = RtanθCSi. The maximum CS deflection angle is designed to be 20°. To ensure that the spring forces of spring 1 and spring 2 do not vanish within the effective deflection range of CS, F0i > 3−0.5KsR is required.
According to Eq. (2), the ith CAU’s x, q, and F(φ) are the motor side displacement θMi, where θMi = θmi/N, the FS angular displacement qi, and the driving torque of the pulley τCAUi, respectively. θmi and N are the angular displacement of motor and the deceleration ratio of the harmonic drive gear, respectively. The following force and motion transfer relationships among CS, FS, and WG are obtained according to harmonic drive principle.
{θWG=(N+1)θCSNθFS,τFS=NN+1τCS,
where θCS, θFS, and θWG are the angular deflections of CS, FS, and WG, respectively, and τCS and τFS are CS torque and FS torque, respectively. Hence, the expressions of qi, φi, and τCAUi are presented as follows:
{qi=N1NθCSi+1Nθmi,φi=θMiqi=θCSi,τCAUi(qi,θMi)=NN+1τCSi=2KsR2tanφi.
Based on the definition of mechanical stiffness in Eq. (2), the stiffness of the ith CAU can be obtained as follows:
KCAUi=τCAUi(qi,θMi)qi=2KsR2cos2(θMiqi).
For nonlinear elastic mechanisms, different φ corresponds to different stiffness values. The φi and the stiffness of the ith CAU are determined by the load on its pulley. The characteristic between the external load and φi of the ith CAU and that between the stiffness and φi of the ith CAU are shown in Fig.9(a) and 9(b), respectively. Adjusting the ith CAU stiffness requires varying its φi. However, a variation of its driving toque is caused at the same time. Therefore, adjusting the stiffness of a CAU actively requires an additional torque to be applied by another. For a fixed stiffness (stiffness value is constant) mechanical device, the mechanical stiffness is independent of compliant deflection even if the external load changes in anyway.
Fig.9 Characteristics of CAU. (a) External load of CAU versus compliance deflection at different pre-compressions and (b) CAU stiffness versus compliance deflection at different pre-compressions.

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The joint differential mechanism couples the motion of two output shafts of CAU to synthesize the motion of two finger joints. Therefore, the ith finger joint torque τJi is a function of φ1 and φ2; thus, τJi can be calculated via position vector Θ (i = 1,2 and Θ = [q1 q2 θM1 θM2]T). Based on the definition of mechanical stiffness in Eq. (2), the expression of the ith finger joint stiffness (KJi) is given by the following:
KJi=τJiθi.
The ith (i = 1,2) CAU output torque based on position vector is obtained as follows:
τCAUi(Θ)=2KsR2tan(θMiqi)=2KsR2tan(θMi+(1)ipaθ1papbθ2).
According to Eqs. (4) and (10), the finger joint torque vector τJ (τJ = [τJ1 τJ2]T) based on the position vector is obtained as follows:
τJ(Θ)=2KsR2TD[tan(θM1paθ1papbθ2)tan(θM2+paθ1papbθ2)].
According to Eq. (2), the finger joint stiffness vector KJ (KJ = [KJ1 KJ2]T) based on position vector is obtained as follows:
KJ(Θ)=2KsR2TD[pacos2(θM1paθ1papbθ2)papbcos2(θM2+paθ1papbθ2)]=2KsR2TD[pacos2(θM1q1)papbcos2(θM2q2)].
The method of deriving finger joint stiffness from position information is described in the previous section. This method is convenient to observe finger stiffness in real time because the position information is easy to measure. However, it involves many variables, which is not conducive to analyzing the variation law of joint stiffness. A functional relationship exists between a mechanical stiffness and its external load. Thus, the mechanical stiffness can be characterized by force information, which facilitates the analysis of stiffness variation; it is also applicable to CAU and finger joints. CAU stiffness and finger joint stiffness based on force information can be solved using a concept called eigen triangle. Eigen triangle is a convenient analysis tool with triangular function characteristics and can be applied to force analysis of various mechanisms, especially in finger mechanisms with complex linear coupling. In the ith CAU, an eigen triangle is a right triangle with a bottom length of 2KsR2 and a height of τCAUi. The sharp angle between the bottom edge and the inclined edge is only φi (i = 1,2), as shown in Fig.10.
Fig.10 Eigen triangle of the CAU statics model.

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Using the eigen triangle, the force-based CAU stiffness (KCAUi) is given by the following:
KCAUi(τCAUi)=2KsR2cos2φ=τCAUi22KsR2+2KsR2.
Equation (13) shows that the stiffness of CAU follows a quadratic variation law. The ith finger joint stiffness based on force (τJ = [τJ1, τJ2]T) is given by the following:
KJi(τJ)=2pa2pb2(i1)KsR2(i=12(τCAUi2KsR2)2+2).
According to Eq. (14), the J1 stiffness characteristic versus τCAU1 and τCAU2 is revealed in Fig.11(a), and the J2 stiffness characteristic versus τCAU1 and τCAU2 is revealed in Fig.11(b).
Fig.11 Simulation results of the finger model. (a) J1 stiffness versus τCAU1 and τCAU2, (b) J2 stiffness versus τCAU1 and τCAU2, and (c) finger potential energy versus τCAU1 and τCAU2.

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3.3 3.3 Potential energy

Potential energy can be calculated by integrating forces into positions, but this method is very complex to implement in the finger.
ECAUi(φi)=0φiτCAUidφi=2KsR2ln|cosφi|=2KsR2ln|cos(θMiqi)|.
Using the eigen triangle, the ith CAU potential energy versus its output torque can be obtained as follows:
ECAUi(τCAUi)=2KsR2ln2KsR2τCAUi2+(2KsR2)2.
However, using position information to solve the potential energy of the entire finger requires a very complex integral operation. Hence, the eigen triangle plays an effective role in the calculation of finger potential energy. Using the Eigen triangle, the finger potential energy Efinger(τJ) based on force information can be obtained as follows:
Efinger(τJ)=2KsR2(i=12ln2KsR2τCAUi2+(2KsR2)2).
According to Eq. (17), the finger potential energy versus τCAU1 and τCAU2 is revealed in Fig.11(c).

3.4 3.4 Changing the finger joint stiffness

Robot fingers should be sufficiently soft to reduce system bandwidth in case of physical impacts to ensure finger system safety, but finger accuracy is decreased under this condition. The adjustment strategy of finger joint stiffness is proposed in this section.
When dexterous hands perform higher-precision operations in sufficiently safe environments, higher finger stiffness is required to improve system bandwidth. Without changing the external load, the adjustment of finger stiffness can be achieved by sacrificing one DOF joint mobility of the finger and switching the finger to VSJ mode through antagonistic motion of two CAUs. The finger stiffness adjusting mode can be divided into distal-joint-locked stiffness adjusting (DSA) mode and proximal-joint-locked stiffness adjusting (PSA) mode by the locked joint, as shown in Fig.12.
Fig.12 Positions of the ith finger joint and the harmonic gear components of the ith CAU in different stiffness adjusting modes.

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1) DSA mode
In DSA operating mode, the distal phalanx is fully abducted or adducted to the J2 mechanical limitation, whereas J1 is mobile, and its stiffness can be actively adjusted.
Case 1: When τCAU1 = τCAU2 < 0, τJ1 = 0, τJ2 < 0, and q1θM1 = q2θM2 > 0, J2 will be fully abducted to its negative mechanical limitation, θ2 = −45°. According to the joint differential principle, q1 + q2 = −0.5iaibπ.
The stiffness vector of J1 and J2 is obtained as follows:
[KJ1KJ2]=[4pa2KsR2cos2(q1θM1)].
Case 2: When τCAU1 = τCAU2 > 0, τJ1 = 0, τJ2 > 0, and q1θM1 = q2θM2 < 0, J2 will be fully adducted to its positive mechanical limitation, θ2 = 90°. According to the joint differential principle, q1 + q2 = iaibπ.
The stiffness vector of J1 and J2 is obtained as follows:
[KJ1KJ2]=[4pa2KsR2cos2(q1θM1)4pa2pb2KsR2cos2(q1θM1)].
2) PSA mode
In PSA mode, the proximal phalanx is fully abducted or adducted to J1 mechanical limitation, whereas J2 is mobile, and its stiffness can be actively adjusted.
Case 1: When τCAU1 + τCAU2 = 0 and τCAU2 < 0 < τCAU1, τJ2 = 0, τJ1 > 0, and q1θM1 = θM2q2 < 0, J1 will be fully adducted to its positive mechanical limitation, θ1 = 90°. According to the joint differential principle, q1q2 = iaπ.
The stiffness vector of J1 and J2 is the same as Eq. (19).
Case 2: When τCAU1 + τCAU2 = 0 and τCAU1 < 0 < τCAU2, τJ1 < 0, τJ2 = 0, and q1θM1 = θM2q2 > 0, J1 will be fully abducted to its negative mechanical limitation, θ1 = −45°. According to the joint differential principle, q1q2 = −0.5iaπ.
[KJ1KJ2]=[4pa2pb2KsR2cos2(q1θM1)].

4 4 Experiments

A finger prototype weighing 480 g was fabricated with alloy material and 3D printed material. The prototype and its controller hardware are shown in Fig.13. A compact, lightweight harmonic gear and a Faulhaber BXT external rotor brushless direct current motor are adopted in each CAU that can provide peak torque of up to 4.1 N∙m at the CAU output shaft, and the maximum fingertip force reaches up to 40 N. The stiffness of CAU is between 3.45 and 4.6 N∙m/rad, and the maximum storable potential energy of a single CAU is 0.5 J. The finger motion is driven by a pair of motors, and its closed loop control is achieved by measuring the position information of the finger via four absolute magnetic encoders (AS5048A) with 14-bit accuracy as feedback. The position sensors at the CAU output side are used as the finger joint feedbacks to realize the closed-loop control of the finger motion, and the networked motion controller is adopted to drive and control the speed of the motor. The PC sends out the motion command of the finger joint, and the STM32 controller calculates the required action of the motor to reach the predetermined position, and then sends the motor motion commands to the motion controller of the network. A proportional plus derivative (PD) controller is adopted for the motion control system of the finger, as shown in Fig.14. The parameters of the control system are annotated in Tab.3.
Tab.3 Parameters of finger motion control system
Variables Notes
Kp Proportional gain of the PD controller
Kd Differential gain of the PD controller
μ1, μ2 Coefficients of coulomb friction of CAU1 and CAU2, respectively
ν1, ν2 Coefficients of sliding friction of CAU1 and CAU2, respectively
JM Motor inertia of deceleration
Fig.13 Prototype of AVS-finger and its controller hardware.

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Fig.14 Finger motion control system and its control effects. (a) Finger motion control block diagram, (b) desired joint trajectories, and (c) position errors of J1 and J2.

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4.1 4.1 Loading and robustness tests

The experiment shown in Fig.15(a) verifies the excellent robustness of the finger mechanism as described in Section 2. Hammering the finger with a 1.5 kg steel hammer in the positive and negative directions of the finger causes no structural damages. Finally, the finger returns to its original position under the action of the motion controller. Fig.15(b) depicts the result of finger loading test. The finger can lift weights of 2 and 4 kg at the fingertip in a fully straightened configuration without any structural damage or motor abnormalities.
Fig.15 Physical impact, lifting, grasping, and manipulating tests. (a) Hammering the finger with a steel hammer at a speed of 1.2 m/s, (b) lifting tests, (c) precise grasping and power grasping, (d) screwing the cap, and (e) clicking the roller of the mouse.

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4.2 4.2 Grasping and manipulation experiments

To assess the internal manipulation performance of the finger, several grasping and manipulating tests are carried out. Fingertip grasping (or precise grasping) and power grasping tests are performed on a group of typical objects in daily life. Cylindrical objects, rectangular objects, and spherical objects of different sizes are selected to guarantee the universality of finger grasping. Precise grasping tests on a 55 mm × 26 mm × 13 mm cuboid, a 26-mm diameter cylinder, and a 13 mm diameter plastic ball are performed, and power grasping tests on a 55 mm × 55 mm × 55 mm cuboid, a 56-mm diameter cylinder, and a 74-mm diameter apple are performed as shown in Fig.15(c).
Fig.15(d) depicts the operation of screwing bottle cap. The cap of the plastic bottle fixed on the workbench is screwed around counterclockwise with the finger. Fig.15(e) depicts the computer mouse manipulation test, in which the roller of the mouse is clicked with the fingertip.

4.3 4.3 Joint stiffness identifications

The stiffness characteristics of two finger joints can be identified by the external load on the joint and the corresponding flexibility deflection angle, and the experimental device is set as shown in Fig.16. A set of weights of the same weight is suspended and removed one by one at the fingertip with the motor position fixed at 0° to measure the two joint deflections. The deflections of the two joint angles are measured by the two magnetic encoders at the CAU output side. The experimental and model results of J1 and J2 are depicted in Fig.16(b) and 16(c), respectively. The existing deviations are mainly caused by the difference of friction between J1 and J2, and also by the offset of the origin of force of the suspended weight on the fingertip.
Fig.16 Model validation of finger joint stiffness characteristics. (a) Experimental setup; experimental and model results of (b) J1 and (c) J2.

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4.4 4.4 Joint stiffness variation

The joint stiffness variation experiment is set up with a 200-g weight dropping freely from a position of 0.3-m high hitting the fingertips in DSA-mode finger configuration and PSA-mode finger configuration, respectively, as shown in Fig.17(a). Larger finger joint stiffness results in smaller joint deflection after physical impact. The change in the joint stiffness can be characterized by the deflection movement of the finger joint during the impact. In DSA-mode finger configuration, the position of J2 is maintained at 90° all the time, and the fingertip is hit with φ1 = φ2 = 0°, φ1 = φ2 = 10°, and φ1 = φ2 = 20°. The experimental results shown in Fig.17(b) reveal that as the modulus of φi (i = 1,2) increases, the stiffness of J1 increases as well as the deflection, resulting in a reduction of the peak J1 deflection under the collision. The experimental results are shown in Fig.17(b). In PSA mode finger configuration, the position of J1 is maintained at 90° all the time, and the fingertip is hit with φ1 = φ2 = 0°, φ1 = ‒φ2 = 10°, and φ1 = ‒φ2 = 20°. The experimental results shown in Fig.17(c) reveal that as the modulus of φi (i = 1,2) increases, the stiffness of the J2 increases as well as the deflection, resulting in a reduction of the peak J1 deflection under the collision. The experimental results are shown in Fig.17(b).
Fig.17 Finger joint stiffness adjusting operation tests. (a) Experimental setup; (b) J1 positions and (c) J2 positions during finger impact with different finger stiffness presets.

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5 5 Conclusions and future work

This paper presented a hardware implementation method, modeling, identification, and stiffness adjusting methods of the AVS-finger based on harmonic driven mechanism and VSA principle. The finger mechanism achieves passive submissiveness to physical impacts and implementation of VSA principles in the finger of the dexterous hand in very compact size without adding supernumerary actuators. The mechanical design and stiffness adjusting operation methods of the AVS-finger were elaborated. Biologically inspired by the biomimetic stiffness variation principle of discarding some mobilities to adjust stiffness, the stiffness adjusting operation methods are achieved by switching a finger joint to its mechanical limitation to adjust finger stiffness. The experimental results of joint deflection with finger impact under different finger stiffness presets were provided. The finger was proven to have excellent mechanical robustness by hammering experiments. Through a series of grasping and manipulation experiments, the satisfactory grasping and manipulation ability of the finger was verified.
In future work, optimization of nonlinear elastic mechanisms in the CAU will be implemented to improve stiffness adjustment range and more detailed model evaluation. Furthermore, structural optimization, lubrication, weight reduction, and compactness will be implemented, and the hardware system of a complete dexterous hand will be designed and fabricated.

References

[1]
Brinksmeier E, Gläbe R, Schönemann L. Review on diamond-machining processes for the generation of functional surface structures. CIRP Journal of Manufacturing Science and Technology, 2012, 5(1): 1–7
CrossRef Google scholar
[2]
Jain V, Ranjan P, Suri V, Chemo-mechanical magneto-rheological finishing (CMMRF) of silicon for microelectronics applications. CIRP Annals-Manufacturing Technology, 2010, 59(1): 323–328
CrossRef Google scholar
[3]
Yamamura K, Takiguchi T, Ueda M, Plasma assisted polishing of single crystal SiC for obtaining atomically flat strain-free surface. CIRP Annals-Manufacturing Technology, 2011, 60(1): 571–574
CrossRef Google scholar
[4]
Schmidt M, Merklein M, Bourell D, Laser based additive manufacturing in industry and academia. CIRP Annals-Manufacturing Technology, 2017, 66(2): 561–583
CrossRef Google scholar
[5]
Hocken R, Chakraborty N, Brown C. Optical metrology of surfaces. CIRP Annals-Manufacturing Technology, 2005, 54(2): 169–183
CrossRef Google scholar
[6]
Savio E, De Chiffre L, Schmitt R. Metrology of freeform shaped parts. CIRP Annals-Manufacturing Technology, 2007, 56(2): 810–835
CrossRef Google scholar
[7]
Zhang X D, Zeng Z, Liu X L, Compensation strategy for machining optical freeform surfaces by the combined on- and off-machine measurement. Optics Express, 2015, 23(19): 24800–24810
CrossRef Google scholar
[8]
Liu X L, Zhang X D, Fang F Z, Identification and compensation of main machining errors on surface form accuracy in ultra-precision diamond turning. International Journal of Machine Tools and Manufacture, 2016, 105: 45–57
CrossRef Google scholar
[9]
Shore P, Cunningham C, DeBra D, Precision engineering for astronomy and gravity science. CIRP Annals-Manufacturing Technology, 2010, 59(2): 694–716
CrossRef Google scholar
[10]
Takaya Y. In-process and on-machine measurement of machining accuracy for process and product quality management: A review. International Journal of Automotive Technology, 2014, 8(1): 4–19
[11]
Lee J C, Shimizu Y, Gao W, Precision evaluation of surface form error of a large-scale roll workpiece on a drum roll lathe. Precision Engineering, 2014, 38(4): 839–848
CrossRef Google scholar
[12]
Novak E, Stout T. Interference microscopes for tribology and corrosion quantification. In: Proceedings of SPIE 6616, Optical Measurement Systems for Industrial Inspection V. Munich: SPIE, 2007, 66163B
CrossRef Google scholar
[13]
Coppola G, Ferraro P, Iodice M, A digital holographic microscope for complete characterization of microelectromechanical systems. Measurement Science and Technology, 2004, 15(3): 529–539
CrossRef Google scholar
[14]
Singh V R, Asundi A. In-line digital holography for dynamic metrology of MEMS. Chinese Optics Letters, 2009, 7(12): 1117–1122
CrossRef Google scholar
[15]
Potcoava M, Kim M. Optical tomography for biomedical applications by digital interference holography. Measurement Science and Technology, 2008, 19(7): 074010
CrossRef Google scholar
[16]
Merola F, Memmolo P, Miccio L, Tomographic flow cytometry by digital holography. Light, Science & Applications, 2017, 6(4): e16241
CrossRef Google scholar
[17]
Fang F Z, Zhang X D, Weckenmann A, Manufacturing and measurement of freeform optics. CIRP Annals-Manufacturing Technology, 2013, 62(2): 823–846
CrossRef Google scholar
[18]
Taylor Hobson Ltd. Form Talysurf PGI Optics Surface Profilometers Brochure. Available from Taylor Hobson website, 2018
[19]
Bruker Corporation. Dimension Icon Atomic Force Microscope Brochure. Available from Bruker website, 2013
[20]
Zygo Corporation. NewViewTM 9000 3D Optical Surface Profiler Brochure. Available from Zygo website, 2018
[21]
OLYMPUS Corporation. LEXT OLS5000 3D Measuring Laser Microscope Brochure. Available from OLYMPUS website, 2018
[22]
Moore Nanotech. Workpiece measurement and Error Compensation System (WECS) Brochure. Available from Moore Nanotech website, 2020
[23]
Vorburger T V, Rhee H G, Renegar T B, Comparison of optical and stylus methods for measurement of surface texture. International Journal of Advanced Manufacturing Technology, 2007, 33(1–2): 110–118
CrossRef Google scholar
[24]
Villarrubia J S. Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation. Journal of Research of the National Institute of Standards and Technology, 1997, 102(4): 425
CrossRef Google scholar
[25]
Wang Y, Xie F, Ma S, Review of surface profile measurement techniques based on optical interferometry. Optics and Lasers in Engineering, 2017, 93: 164–170
CrossRef Google scholar
[26]
Nomura T, Yoshikawa K, Tashiro H, On-machine shape measurement of workpiece surface with Fizeau interferometer. Precision Engineering, 1992, 14(3): 155–159
CrossRef Google scholar
[27]
Shore P, Morantz P, Lee D, Manufacturing and measurement of the MIRI spectrometer optics for the James Webb space telescope. CIRP Annals-Manufacturing Technology, 2006, 55(1): 543–546
CrossRef Google scholar
[28]
Jiang X. In situ real-time measurement for micro-structured surfaces. CIRP Annals-Manufacturing Technology, 2011, 60(1): 563–566
CrossRef Google scholar
[29]
Wang D, Fu X, Xu P, Compact snapshot dual-mode interferometric system for on-machine measurement. Optics and Lasers in Engineering, 2020, 132: 106129
CrossRef Google scholar
[30]
Gao W, Haitjema H, Fang F Z, On-machine and in-process surface metrology for precision manufacturing. CIRP Annals-Manufacturing Technology, 2019, 68(2): 843–866
CrossRef Google scholar
[31]
Li D, Wang B, Tong Z, On-machine surface measurement and applications for ultra-precision machining: A state-of-the-art review. International Journal of Advanced Manufacturing Technology, 2019, 104(1–4): 831–847
CrossRef Google scholar
[32]
de Groot P. Principles of interference microscopy for the measurement of surface topography. Advances in Optics and Photonics, 2015, 7(1): 1–65
CrossRef Google scholar
[33]
Zuo C, Feng S, Huang L, Phase shifting algorithms for fringe projection profilometry: A review. Optics and Lasers in Engineering, 2018, 109: 23–59
CrossRef Google scholar
[34]
Malacara D. Optical Shop Testing. Hoboken: John Wiley & Sons, 2007, 547–666
[35]
Creath K. V phase-measurement interferometry techniques. Progress in Optics, 1988, 26: 349–393
CrossRef Google scholar
[36]
Cheng Y Y, Wyant J C. Multiple-wavelength phase-shifting interferometry. Applied Optics, 1985, 24(6): 804–807
CrossRef Google scholar
[37]
Lannes A. Integer ambiguity resolution in phase closure imaging. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 2001, 18(5): 1046–1055
CrossRef Google scholar
[38]
Fornaro G, Franceschetti G, Lanari R, Robust phase-unwrapping techniques: A comparison. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 1996, 13(12): 2355–2366
CrossRef Google scholar
[39]
Davé D P, Akkin T, Milner T E, Phase-sensitive frequency-multiplexed optical low-coherence reflectometery. Optics Communications, 2001, 193(1–6): 39–43
CrossRef Google scholar
[40]
Wyant J C. White light interferometry. Proceedings of SPIE 4737, Holography: A Tribute to Yuri Denisyuk and Emmett Leith, 2002, 98–108
CrossRef Google scholar
[41]
Cheng Y Y, Wyant J C. Two-wavelength phase shifting interferometry. Applied Optics, 1984, 23(24): 4539–4543
CrossRef Google scholar
[42]
Onodera R, Ishii Y. Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes. Applied Optics, 1994, 33(22): 5052–5061
CrossRef Google scholar
[43]
Abdelsalam D, Kim D. Two-wavelength in-line phase-shifting interferometry based on polarizing separation for accurate surface profiling. Applied Optics, 2011, 50(33): 6153–6161
CrossRef Google scholar
[44]
Decker J E, Miles J R, Madej A A, Increasing the range of unambiguity in step-height measurement with multiple-wavelength interferometry—Application to absolute long gauge block measurement. Applied Optics, 2003, 42(28): 5670–5678
CrossRef Google scholar
[45]
Warnasooriya N, Kim M. LED-based multi-wavelength phase imaging interference microscopy. Optics Express, 2007, 15(15): 9239–9247
CrossRef Google scholar
[46]
Schmit J, Hariharan P. Two-wavelength interferometric profilometry with a phase-step error-compensating algorithm. Optical Engineering, 2006, 45(11): 115602
CrossRef Google scholar
[47]
Pförtner A, Schwider J. Red-green-blue interferometer for the metrology of discontinuous structures. Applied Optics, 2003, 42(4): 667–673
CrossRef Google scholar
[48]
Upputuri P K, Mohan N K, Kothiyal M P. Measurement of discontinuous surfaces using multiple-wavelength interferometry. Optical Engineering, 2009, 48(7): 073603
CrossRef Google scholar
[49]
Caber P J. Interferometric profiler for rough surfaces. Applied Optics, 1993, 32(19): 3438–3441
CrossRef Google scholar
[50]
Sandoz P, Devillers R, Plata A. Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry. Journal of Modern Optics, 1997, 44(3): 519–534
CrossRef Google scholar
[51]
Debnath S K, Kothiyal M P. Experimental study of the phase-shift miscalibration error in phase-shifting interferometry: Use of a spectrally resolved white-light interferometer. Applied Optics, 2007, 46(22): 5103–5109
CrossRef Google scholar
[52]
Yang C, Wax A, Dasari R R, 2π ambiguity-free optical distance measurement with subnanometer precision with a novel phase-crossing low-coherence interferometer. Optics Letters, 2002, 27(2): 77–79
CrossRef Google scholar
[53]
Deck L, de Groot P. High-speed noncontact profiler based on scanning white-light interferometry. Applied Optics, 1994, 33(31): 7334–7338
CrossRef Google scholar
[54]
Harasaki A, Schmit J, Wyant J C. Improved vertical-scanning interferometry. Applied Optics, 2000, 39(13): 2107–2115
CrossRef Google scholar
[55]
Balasubramanian N. US Patent, 4340306, 1982-07-20
[56]
Kumar U P, Haifeng W, Mohan N K, White light interferometry for surface profiling with a colour CCD. Optics and Lasers in Engineering, 2012, 50(8): 1084–1088
CrossRef Google scholar
[57]
Gianto G, Salzenstein F, Montgomery P. Comparison of envelope detection techniques in coherence scanning interferometry. Applied Optics, 2016, 55(24): 6763–6774
CrossRef Google scholar
[58]
Gianto G, Montgomery P, Salzenstein F, Study of robustness of 2D fringe processing in coherence scanning interferometry for the characterization of a transparent polymer film. In: Proceedings of 2016 International Conference on Instrumentation, Control and Automation (ICA). Bandung: IEEE, 2016, 60–65
CrossRef Google scholar
[59]
Zhou Y, Cai H, Zhong L, Eliminating the influence of source spectrum of white light scanning interferometry through time-delay estimation algorithm. Optics Communications, 2017, 391: 1–8
CrossRef Google scholar
[60]
de Groot P. Coherence scanning interferometry. In: Leach R, ed. Optical Measurement of Surface Topography. Berlin: Springer, 2011, 187–208
CrossRef Google scholar
[61]
Fang F Z, Zeng Z, Zhang X D, Measurement of micro-V-groove dihedral using white light interferometry. Optics Communications, 2016, 359: 297–303
CrossRef Google scholar
[62]
de Groot P, Deck L. Surface profiling by analysis of white-light interferograms in the spatial frequency domain. Journal of Modern Optics, 1995, 42(2): 389–401
CrossRef Google scholar
[63]
Kino G S, Chim S S. Mirau correlation microscope. Applied Optics, 1990, 29(26): 3775–3783
CrossRef Google scholar
[64]
Bowe B W, Toal V. White light interferometric surface profiler. Optical Engineering, 1998, 37(6): 1796–1800
CrossRef Google scholar
[65]
Lehmann P, Tereschenko S, Xie W. Fundamental aspects of resolution and precision in vertical scanning white-light interferometry. Surface Topography: Metrology and Properties, 2016, 4(2): 024004
CrossRef Google scholar
[66]
Yamaguchi I, Yamamoto A, Yano M. Surface topography by wavelength scanning interferometry. Optical Engineering, 2000, 39(1): 40–47
CrossRef Google scholar
[67]
Yamamoto A, Yamaguchi I. Profilometry of sloped plane surfaces by wavelength scanning interferometry. Optical Review, 2002, 9(3): 112–121
CrossRef Google scholar
[68]
Kuwamura S, Yamaguchi I. Wavelength scanning profilometry for real-time surface shape measurement. Applied Optics, 1997, 36(19): 4473–4482
CrossRef Google scholar
[69]
Yamamoto A, Kuo C C, Sunouchi K, Surface shape measurement by wavelength scanning interferometry using an electronically tuned Ti: Sapphire laser. Optical Review, 2001, 8(1): 59–63
CrossRef Google scholar
[70]
Yamamoto A, Yamaguchi I. Surface profilometry by wavelength scanning Fizeau interferometer. Optics & Laser Technology, 2000, 32(4): 261–266
CrossRef Google scholar
[71]
Ishii Y. Wavelength-tunable laser-diode interferometer. Optical Review, 1999, 6(4): 273–283
CrossRef Google scholar
[72]
Jiang X, Wang K, Gao F, Fast surface measurement using wavelength scanning interferometry with compensation of environmental noise. Applied Optics, 2010, 49(15): 2903–2909
CrossRef Google scholar
[73]
Muhamedsalih H, Jiang X, Gao F. Comparison of fast Fourier transform and convolution in wavelength scanning interferometry. Proceedings of SPIE 8082, Optical Measurement Systems for Industrial Inspection VII, 2011, 8082: 80820Q
CrossRef Google scholar
[74]
Gao F, Muhamedsalih H, Jiang X. Surface and thickness measurement of a transparent film using wavelength scanning interferometry. Optics Express, 2012, 20(19): 21450–21456
CrossRef Google scholar
[75]
Muhamedsalih H, Jiang X, Gao F. Accelerated surface measurement using wavelength scanning interferometer with compensation of environmental noise. Procedia CIRP, 2013, 10: 70–76
CrossRef Google scholar
[76]
Moschetti G, Forbes A, Leach R K, Phase and fringe order determination in wavelength scanning interferometry. Optics Express, 2016, 24(8): 8997–9012
CrossRef Google scholar
[77]
Zhang T, Gao F, Jiang X. Surface topography acquisition method for double-sided near-right-angle structured surfaces based on dual-probe wavelength scanning interferometry. Optics Express, 2017, 25(20): 24148–24156
CrossRef Google scholar
[78]
Zhang T, Gao F, Muhamedsalih H, Improvement of the fringe analysis algorithm for wavelength scanning interferometry based on filter parameter optimization. Applied Optics, 2018, 57(9): 2227–2234
CrossRef Google scholar
[79]
Swanson E A, Huang D, Hee M R, High-speed optical coherence domain reflectometry. Optics Letters, 1992, 17(2): 151–153
CrossRef Google scholar
[80]
Huang Y C, Chou C, Chou L Y, Polarized optical heterodyne profilometer. Japanese Journal of Applied Physics, 1998, 37(Part 1, No. 1): 351–354
CrossRef Google scholar
[81]
Zhao H, Liang R, Li D, Practical common-path heterodyne surface profiling interferometer with automatic focusing. Optics & Laser Technology, 2001, 33(4): 259–265
CrossRef Google scholar
[82]
Demarest F C. High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics. Measurement Science & Technology, 1998, 9(7): 1024–1030
CrossRef Google scholar
[83]
Xie Y, Wu Y. Zeeman laser interferometer errors for high-precision measurements. Applied Optics, 1992, 31(7): 881–884
CrossRef Google scholar
[84]
Gelmini E, Minoni U, Docchio F. Tunable, double-wavelength heterodyne detection interferometer for absolute-distance measurements. Optics Letters, 1994, 19(3): 213–215
CrossRef Google scholar
[85]
Park Y, Cho K. Heterodyne interferometer scheme using a double pass in an acousto-optic modulator. Optics Letters, 2011, 36(3): 331–333
CrossRef Google scholar
[86]
Matsumoto H, Hirai A. A white-light interferometer using a lamp source and heterodyne detection with acousto-optic modulators. Optics Communications, 1999, 170(4–6): 217–220
CrossRef Google scholar
[87]
Hirai A, Matsumoto H. High-sensitivity surface-profile measurements by heterodyne white-light interferometer. Optical Engineering, 2001, 40(3): 387–392
CrossRef Google scholar
[88]
Dai X, Katuo S. High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry. Measurement Science & Technology, 1998, 9(7): 1031–1035
CrossRef Google scholar
[89]
Xu X, Wang Y, Ji Y, A novel dual-wavelength iterative method for generalized dual-wavelength phase-shifting interferometry with second-order harmonics. Optics and Lasers in Engineering, 2018, 106: 39–46
CrossRef Google scholar
[90]
Deck L L. Fourier-transform phase-shifting interferometry. Applied Optics, 2003, 42(13): 2354–2365
CrossRef Google scholar
[91]
Kafri O. Fundamental limit on accuracy in interferometry. Optics Letters, 1989, 14(13): 657–658
CrossRef Google scholar
[92]
Zhai Z, Li Z, Zhang Y, An accurate phase shift extraction algorithm for phase shifting interferometry. Optics Communications, 2018, 429: 144–151
CrossRef Google scholar
[93]
Vo Q, Fang F Z, Zhang X D, Surface recovery algorithm in white light interferometry based on combined white light phase shifting and fast Fourier transform algorithms. Applied Optics, 2017, 56(29): 8174–8185
CrossRef Google scholar
[94]
Chou C, Shyu J, Huang Y, Common-path optical heterodyne profilometer: A configuration. Applied Optics, 1998, 37(19): 4137–4142
CrossRef Google scholar
[95]
Chang W Y, Chen K H, Chen D C, Heterodyne moiré interferometry for measuring corneal surface profile. Optics and Lasers in Engineering, 2014, 54: 232–235
CrossRef Google scholar
[96]
Ajithaprasad S, Gannavarpu R. Non-invasive precision metrology using diffraction phase microscopy and space-frequency method. Optics and Lasers in Engineering, 2018, 109: 17–22
CrossRef Google scholar
[97]
Venkata Satya Vithin A, Ajithaprasad S, Rajshekhar G. Step phase reconstruction using an anisotropic total variation regularization method in a diffraction phase microscopy. Applied Optics, 2019, 58(26): 7189–7194
CrossRef Google scholar
[98]
Rajshekhar G, Bhaduri B, Edwards C, Nanoscale topography and spatial light modulator characterization using wide-field quantitative phase imaging. Optics Express, 2014, 22(3): 3432–3438
CrossRef Google scholar
[99]
Larkin K G. Efficient nonlinear algorithm for envelope detection in white light interferometry. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 1996, 13(4): 832–843
CrossRef Google scholar
[100]
Kim J H, Yoon S W, Lee J H, New algorithm of white-light phase shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor. Optics and Lasers in Engineering, 2008, 46(2): 140–148
CrossRef Google scholar
[101]
Tien C L, Yu K C, Tsai T Y, Measurement of surface roughness of thin films by a hybrid interference microscope with different phase algorithms. Applied Optics, 2014, 53(29): H213–H219
CrossRef Google scholar
[102]
Lei Z, Liu X, Chen L, A novel surface recovery algorithm in white light interferometry. Measurement, 2016, 80: 1–11
CrossRef Google scholar
[103]
Muhamedsalih H, Gao F, Jiang X. Comparison study of algorithms and accuracy in the wavelength scanning interferometry. Applied Optics, 2012, 51(36): 8854–8862
CrossRef Google scholar
[104]
Sandoz P. Wavelet transform as a processing tool in white-light interferometry. Optics Letters, 1997, 22(14): 1065–1067
CrossRef Google scholar
[105]
Recknagel R J, Notni G. Analysis of white light interferograms using wavelet methods. Optics Communications, 1998, 148(1–3): 122–128
CrossRef Google scholar
[106]
Hart M, Vass D G, Begbie M L. Fast surface profiling by spectral analysis of white-light interferograms with Fourier transform spectroscopy. Applied Optics, 1998, 37(10): 1764–1769
CrossRef Google scholar
[107]
Freischlad K, Koliopoulos C L. Fourier description of digital phase-measuring interferometry. Journal of the Optical Society of America. A, Optics and Image Science, 1990, 7(4): 542–551
CrossRef Google scholar
[108]
Larkin K, Oreb B. Design and assessment of symmetrical phase-shifting algorithms. Journal of the Optical Society of America. A, Optics and Image Science, 1992, 9(10): 1740–1748
CrossRef Google scholar
[109]
de Groot P. Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window. Applied Optics, 1995, 34(22): 4723–4730
CrossRef Google scholar
[110]
Schmit J, Creath K. Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry. Applied Optics, 1995, 34(19): 3610–3619
CrossRef Google scholar
[111]
Kumar U P, Bhaduri B, Kothiyal M, Two-wavelength micro-interferometry for 3-D surface profiling. Optics and Lasers in Engineering, 2009, 47(2): 223–229
CrossRef Google scholar
[112]
Bankhead A D, McDonnell I. US Patent, 7385707, 2008-06-10
[113]
Ai C, Novak E L. US Patent, 5633715, 1997-05-27
[114]
Chen S, Palmer A, Grattan K, Fringe order identification in optical fibre white-light interferometry using centroid algorithm method. Electronics Letters, 1992, 28(6): 553–555
CrossRef Google scholar
[115]
Alexander B F, Ng K C. Elimination of systematic error in subpixel accuracy centroid estimation. Optical Engineering, 1991, 30(9): 1320–1332
CrossRef Google scholar
[116]
Harasaki A, Wyant J C. Fringe modulation skewing effect in white-light vertical scanning interferometry. Applied Optics, 2000, 39(13): 2101–2106
CrossRef Google scholar
[117]
Suematsu M, Takeda M. Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis. Applied Optics, 1991, 30(28): 4046–4055
CrossRef Google scholar
[118]
Takeda M, Ina H, Kobayashi S. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. Journal of the Optical Society of America, 1982, 72(1): 156–160
CrossRef Google scholar
[119]
Takeda M, Mutoh K. Fourier transform profilometry for the automatic measurement of 3-D object shapes. Applied Optics, 1983, 22(24): 3977
CrossRef Google scholar
[120]
Su X, Chen W. Fourier transform profilometry: A review. Optics and Lasers in Engineering, 2001, 35(5): 263–284
CrossRef Google scholar
[121]
Chim S S, Kino G S. Correlation microscope. Optics Letters, 1990, 15(10): 579–581
CrossRef Google scholar
[122]
Chim S S, Kino G S. Phase measurements using the Mirau correlation microscope. Applied Optics, 1991, 30(16): 2197–2201
CrossRef Google scholar
[123]
Trusiak M, Wielgus M, Patorski K. Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition. Optics and Lasers in Engineering, 2014, 52: 230–240
CrossRef Google scholar
[124]
Huang L, Kemao Q, Pan B, Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry. Optics and Lasers in Engineering, 2010, 48(2): 141–148
CrossRef Google scholar
[125]
Kemao Q. Applications of windowed Fourier fringe analysis in optical measurement: A review. Optics and Lasers in Engineering, 2015, 66: 67–73
CrossRef Google scholar
[126]
Kemao Q. Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations. Optics and Lasers in Engineering, 2007, 45(2): 304–317
CrossRef Google scholar
[127]
Kemao Q, Wang H, Gao W. Windowed Fourier transform for fringe pattern analysis: Theoretical analyses. Applied Optics, 2008, 47(29): 5408–5419
CrossRef Google scholar
[128]
Kemao Q. Windowed Fourier transform for fringe pattern analysis. Applied Optics, 2004, 43(13): 2695–2702
CrossRef Google scholar
[129]
Zweig D A, Hufnagel R E. Hilbert transform algorithm for fringe-pattern analysis. Proceedings of SPIE 1333, Advanced Optical Manufacturing and Testing, 1990, 1333: 295–303
CrossRef Google scholar
[130]
Chim S S, Kino G S. Three-dimensional image realization in interference microscopy. Applied Optics, 1992, 31(14): 2550–2553
CrossRef Google scholar
[131]
Zhao Y, Chen Z, Ding Z, Real-time phase-resolved functional optical coherence tomography by use of optical Hilbert transformation. Optics Letters, 2002, 27(2): 98–100
CrossRef Google scholar
[132]
Onodera R, Watanabe H, Ishii Y. Interferometric phase-measurement using a one-dimensional discrete Hilbert transform. Optical Review, 2005, 12(1): 29–36
CrossRef Google scholar
[133]
Li M, Quan C, Tay C. Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry. Optics & Laser Technology, 2008, 40(7): 920–929
CrossRef Google scholar
[134]
Li S, Su X, Chen W. Wavelet ridge techniques in optical fringe pattern analysis. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 2010, 27(6): 1245–1254
CrossRef Google scholar
[135]
Watkins L, Tan S, Barnes T. Determination of interferometer phase distributions by use of wavelets. Optics Letters, 1999, 24(13): 905–907
CrossRef Google scholar
[136]
Zhong J, Weng J. Phase retrieval of optical fringe patterns from the ridge of a wavelet transform. Optics Letters, 2005, 30(19): 2560–2562
CrossRef Google scholar
[137]
de Groot P J, Deck L L. Surface profiling by frequency-domain analysis of white light interferograms. Proceedings of SPIE 2248, Optical Measurements and Sensors for the Process Industries, 1994, 2248: 101–105
CrossRef Google scholar
[138]
de Groot P, Colonna de Lega X, Kramer J, Determination of fringe order in white-light interference microscopy. Applied Optics, 2002, 41(22): 4571–4578
CrossRef Google scholar
[139]
de Groot P, Colonna de Lega X. Signal modeling for low-coherence height-scanning interference microscopy. Applied Optics, 2004, 43(25): 4821–4830
CrossRef Google scholar
[140]
Zhang S. Recent progresses on real-time 3D shape measurement using digital fringe projection techniques. Optics and Lasers in Engineering, 2010, 48(2): 149–158
CrossRef Google scholar
[141]
Hariharan P, Oreb B, Eiju T. Digital phase-shifting interferometry: A simple error-compensating phase calculation algorithm. Applied Optics, 1987, 26(13): 2504–2506
CrossRef Google scholar
[142]
Sandoz P. An algorithm for profilometry by white-light phase-shifting interferometry. Journal of Modern Optics, 1996, 43(8): 1545–1554
CrossRef Google scholar
[143]
de Groot P J. Long-wavelength laser diode interferometer for surface flatness measurement. Proceedings of SPIE 2248, Optical Measurements and Sensors for the Process Industries, 1994, 2248: 136–141
CrossRef Google scholar
[144]
Dong Z, Chen Z. Advanced Fourier transform analysis method for phase retrieval from a single-shot spatial carrier fringe pattern. Optics and Lasers in Engineering, 2018, 107: 149–160
CrossRef Google scholar
[145]
Ma S, Quan C, Zhu R, Micro-profile measurement based on windowed Fourier transform in white-light scanning interferometry. Optics Communications, 2011, 284(10–11): 2488–2493
CrossRef Google scholar
[146]
Ma S, Quan C, Zhu R, Application of least-square estimation in white-light scanning interferometry. Optics and Lasers in Engineering, 2011, 49(7): 1012–1018
CrossRef Google scholar
[147]
Zhang Z, Jing Z, Wang Z, Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry. Optics and Lasers in Engineering, 2012, 50(8): 1152–1160
CrossRef Google scholar
[148]
Huang J, Chen W, Su X. Application of two-dimensional wavelet transform in the modulation measurement profilometry. Optical Engineering, 2017, 56(3): 034105
CrossRef Google scholar
[149]
Serizawa T, Suzuki T, Choi S, 3-D surface profile measurement using spectral interferometry based on continuous wavelet transform. Optics Communications, 2017, 396: 216–220
CrossRef Google scholar
[150]
de Groot P J. 101-frame algorithm for phase-shifting interferometry. Proceedings of SPIE 3098, Optical Inspection and Micromeasurements II, 1997, 3098: 283–293
CrossRef Google scholar
[151]
Shen M H, Hwang C H, Wang W C. Center wavelength measurement based on higher steps phase-shifting algorithms in white-light scanning interferometry. Procedia Engineering, 2014, 79: 447–455
CrossRef Google scholar
[152]
Shen M H, Hwang C H, Wang W C. Using higher steps phase-shifting algorithms and linear least-squares fitting in white-light scanning interferometry. Optics and Lasers in Engineering, 2015, 66: 165–173
CrossRef Google scholar
[153]
Sifuzzaman M, Islam M, Ali M. Application of wavelet transform and its advantages compared to Fourier transform. Journal of Physiological Sciences, 2009, 13: 121–134
[154]
Wei D, Xiao M, Yang P. Do we need all the frequency components of a fringe signal to obtain position information in a vertical scanning wideband interferometer? Optics Communications, 2019, 430: 234–237
CrossRef Google scholar
[155]
Wei D, Aketagawa M. Automatic selection of frequency domain filter for interference fringe analysis in pulse-train interferometer. Optics Communications, 2018, 425: 113–117
CrossRef Google scholar
[156]
Pavliček P, Michalek V. White-light interferometry—Envelope detection by Hilbert transform and influence of noise. Optics and Lasers in Engineering, 2012, 50(8): 1063–1068
CrossRef Google scholar
[157]
Huang N E, Shen Z, Long S R, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 1998, 454(1971): 903–995
[158]
Trusiak M, Patorski K, Pokorski K. Hilbert-Huang processing for single-exposure two-dimensional grating interferometry. Optics Express, 2013, 21(23): 28359–28379
CrossRef Google scholar
[159]
Trusiak M, Służewski Ł, Patorski K. Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis. Optics Express, 2016, 24(4): 4221–4238
CrossRef Google scholar
[160]
Trusiak M, Mico V, Garcia J, Quantitative phase imaging by single-shot Hilbert-Huang phase microscopy. Optics Letters, 2016, 41(18): 4344–4347
CrossRef Google scholar
[161]
Deepan B, Quan C, Tay C. Determination of phase derivatives from a single fringe pattern using Teager Hilbert Huang transform. Optics Communications, 2016, 359: 162–170
CrossRef Google scholar
[162]
Trusiak M, Styk A, Patorski K. Hilbert–Huang transform based advanced Bessel fringe generation and demodulation for full-field vibration studies of specular reflection micro-objects. Optics and Lasers in Engineering, 2018, 110: 100–112
CrossRef Google scholar
[163]
Deng J, Wu D, Wang K, Precise phase retrieval under harsh conditions by constructing new connected interferograms. Scientific Reports, 2016, 6(1): 24416
CrossRef Google scholar
[164]
Rajshekhar G, Rastogi P. Multiple signal classification technique for phase estimation from a fringe pattern. Applied Optics, 2012, 51(24): 5869–5875
CrossRef Google scholar
[165]
Rajshekhar G, Rastogi P. Fringe demodulation using the two-dimensional phase differencing operator. Optics Letters, 2012, 37(20): 4278–4280
CrossRef Google scholar
[166]
Vishnoi A, Ramaiah J, Rajshekhar G. Phase recovery method in digital holographic interferometry using high-resolution signal parameter estimation. Applied Optics, 2019, 58(6): 1485–1490
CrossRef Google scholar
[167]
Feng S, Chen Q, Gu G, Fringe pattern analysis using deep learning. Advanced Photonics, 2019, 1(2): 025001
CrossRef Google scholar
[168]
Gomez C, Su R, de Groot P, Noise reduction in coherence scanning interferometry for surface topography measurement. Nanomanufacturing and Metrology, 2020, 3(1): 68–76
CrossRef Google scholar
[169]
Gdeisat M, Burton D, Lilley F, Fast fringe pattern phase demodulation using FIR Hilbert transformers. Optics Communications, 2016, 359: 200–206
CrossRef Google scholar
[170]
Zhong M, Chen F, Xiao C, 3-D surface profilometry based on modulation measurement by applying wavelet transform method. Optics and Lasers in Engineering, 2017, 88: 243–254
CrossRef Google scholar
[171]
Bernal O D, Seat H C, Zabit U, Robust detection of non-regular interferometric fringes from a self-mixing displacement sensor using bi-wavelet transform. IEEE Sensors Journal, 2016, 16(22): 7903–7910
CrossRef Google scholar
[172]
Rajshekhar G, Rastogi P. Phase estimation using a state-space approach based method. Optics and Lasers in Engineering, 2013, 51(8): 1004–1007
CrossRef Google scholar
[173]
Gurov I, Volynsky M. Interference fringe analysis based on recurrence computational algorithms. Optics and Lasers in Engineering, 2012, 50(4): 514–521
CrossRef Google scholar
[174]
Gao W, Huyen N T T, Loi H S, Real-time 2D parallel windowed Fourier transform for fringe pattern analysis using graphics processing unit. Optics Express, 2009, 17(25): 23147–23152
CrossRef Google scholar
[175]
Vishnoi A, Rajshekhar G. Rapid deformation analysis in digital holographic interferometry using graphics processing unit accelerated Wigner-Ville distribution. Applied Optics, 2019, 58(16): 4420–4424
CrossRef Google scholar
[176]
Ramaiah J, Ajithaprasad S, Rajshekhar G. Graphics processing unit assisted diffraction phase microscopy for fast non-destructive metrology. Measurement Science & Technology, 2019, 30(12): 125202
CrossRef Google scholar
[177]
Hariharan P. Phase-shifting interferometry: Minimization of systematic errors. Optical Engineering, 2000, 39(4): 967–970
CrossRef Google scholar
[178]
de Groot P J. Correlated errors in phase-shifting laser Fizeau interferometry. Applied Optics, 2014, 53(19): 4334–4342
CrossRef Google scholar
[179]
Kim Y, Hibino K, Sugita N, Error-compensating phase-shifting algorithm for surface shape measurement of transparent plate using wavelength-tuning Fizeau interferometer. Optics and Lasers in Engineering, 2016, 86: 309–316
CrossRef Google scholar
[180]
Wang Z, Han B. Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms. Optics Letters, 2004, 29(14): 1671–1673
CrossRef Google scholar
[181]
Wang Z, Han B. Advanced iterative algorithm for randomly phase-shifted interferograms with intra- and inter-frame intensity variations. Optics and Lasers in Engineering, 2007, 45(2): 274–280
CrossRef Google scholar
[182]
Cai L, Liu Q, Yang X. Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps. Optics Letters, 2003, 28(19): 1808–1810
CrossRef Google scholar
[183]
Cai L Z, Liu Q, Yang X L. Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors. Optics Communications, 2004, 233(1–3): 21–26
CrossRef Google scholar
[184]
Gao P, Yao B L, Lindlein N, Phase-shift extraction for generalized phase-shifting interferometry. Optics Letters, 2009, 34(22): 3553–3555
CrossRef Google scholar
[185]
Zhang X, Wang J, Zhang X, Correction of phase-shifting error in wavelength scanning digital holographic microscopy. Measurement Science and Technology, 2018, 29(5): 055002
CrossRef Google scholar
[186]
Larkin K G. A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns. Optics Express, 2001, 9(5): 236–253
CrossRef Google scholar
[187]
Guo H, Yu Y, Chen M. Blind phase shift estimation in phase-shifting interferometry. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 2007, 24(1): 25–33
CrossRef Google scholar
[188]
Guo H. Blind self-calibrating algorithm for phase-shifting interferometry by use of cross-bispectrum. Optics Express, 2011, 19(8): 7807–7815
CrossRef Google scholar
[189]
Wang Y, Lu X, Liu Y, Self-calibration phase-shifting algorithm with interferograms containing very few fringes based on Fourier domain estimation. Optics Express, 2017, 25(24): 29971–29982
CrossRef Google scholar
[190]
Cao S, Wang Y, Lu X, Advanced spatial spectrum fitting algorithm for significantly improving the noise resistance ability of self-calibration phase shifting interferometry. Optics and Lasers in Engineering, 2019, 112: 170–181
CrossRef Google scholar
[191]
Ghim Y S, Rhee H G, Davies A, 3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry. Optics Express, 2014, 22(5): 5098–5105
CrossRef Google scholar
[192]
Fuerschbach K, Thompson K P, Rolland J P. Interferometric measurement of a concave, ϕ-polynomial, Zernike mirror. Optics Letters, 2014, 39(1): 18–21
CrossRef Google scholar
[193]
Leong-Hoï A, Claveau R, Flury M, Detection of defects in a transparent polymer with high resolution tomography using white light scanning interferometry and noise reduction. Proceedings of SPIE 9528, Videometrics, Range Imaging, and Applications XIII, 2015, 9528: 952807
CrossRef Google scholar
[194]
Zhou R, Edwards C, Arbabi A, Detecting 20 nm wide defects in large area nanopatterns using optical interferometric microscopy. Nano Letters, 2013, 13(8): 3716–3721
CrossRef Google scholar
[195]
Guo T, Gu Y, Chen J, Surface topography measurement based on color images processing in white light interferometry. Proceedings of SPIE 9525, Optical Measurement Systems for Industrial Inspection IX, 2015, 9525: 952511
CrossRef Google scholar
[196]
Servin M, Quiroga J A, Padilla M. Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications. Weinheim: John Wiley & Sons, 2014, 57–145
[197]
Petrov N V, Skobnikov V A, Shevkunov I A, Features of surface contouring by digital holographic interferometry with tilt of the object illumination. Proceedings of SPIE 10749, Interferometry XIX, 2018, 10749: 1074906
CrossRef Google scholar
[198]
Schmit J, Olszak A G. Challenges in white-light phase-shifting interferometry. Proceedings of SPIE 4777, Interferometry XI: Techniques and Analysis, 2002, 4777: 118–127
CrossRef Google scholar
[199]
Petzing J N, Coupland J M, Leach R K. The Measurement of Rough Surface Topography Using Coherence Scanning Interferometry. NPL Measurement Good Practice Guide 116. Middlesex: Queen’s Printer and Controller of HMSO, 2010, 91–110
[200]
Fay M F, Colonna de Lega X, de Groot P. Measuring high-slope and super-smooth optics with high-dynamic-range coherence scanning interferometry. In: Proceedings of Optical Fabrication and Testing. Hawaii: Optical Society of America, 2014, OW1B.3
CrossRef Google scholar
[201]
Marinello F, Bariani P, Pasquini A, Increase of maximum detectable slope with optical profilers, through controlled tilting and image processing. Measurement Science & Technology, 2007, 18(2): 384–389
CrossRef Google scholar
[202]
de Groot P J. Vibration in phase-shifting interferometry. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 1995, 12(2): 354–365
CrossRef Google scholar
[203]
Wiersma J T, Wyant J C. Vibration insensitive extended range interference microscopy. Applied Optics, 2013, 52(24): 5957–5961
CrossRef Google scholar
[204]
Liu Q, Li L, Zhang H, Simultaneous dual-wavelength phase-shifting interferometry for surface topography measurement. Optics and Lasers in Engineering, 2020, 124: 105813
CrossRef Google scholar
[205]
Li Y, Kästner M, Reithmeier E. Vibration-insensitive low coherence interferometer (LCI) for the measurement of technical surfaces. Measurement, 2017, 104: 36–42
CrossRef Google scholar
[206]
Liu Q, Huang W, Li L, Vibration-resistant interferometric measurement of optical surface figure and roughness. Proceedings of SPIE 11383, Sixth Asia Pacific Conference on Optics Manufacture, 2020, 11383: 1138304
CrossRef Google scholar
[207]
Colonna de Lega X, de Groot P. Lateral resolution and instrument transfer function as criteria for selecting surface metrology instruments. In: Proceedings of Optical Fabrication and Testing. Monterey: Optical Society of America, 2012, OTu1D.4
[208]
de Groot P, Colonna de Lega X, Sykora D, The meaning and measure of lateral resolution for surface profiling interferometers. Optics and Photonics News, 2012, 23(4): 10–13
[209]
Indebetouw G, Tada Y, Rosen J, Brooker G. Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms. Applied Optics, 2007, 46(6): 993–1000
CrossRef Google scholar
[210]
Dong J, Jia S, Jiang C. Surface shape measurement by multi-illumination lensless Fourier transform digital holographic interferometry. Optics Communications, 2017, 402: 91–96
CrossRef Google scholar
[211]
Merola F, Paturzo M, Coppola S, Self-patterning of a polydimethylsiloxane microlens array on functionalized substrates and characterization by digital holography. Journal of Micromechanics and Microengineering, 2009, 19(12): 125006
CrossRef Google scholar
[212]
Bray M. Stitching interferometer for large Plano optics using a standard interferometer. Proceedings of SPIE 3134, Optical Manufacturing and Testing II, 1997, 3134: 39–51
CrossRef Google scholar
[213]
Otsubo M, Okada K, Tsujiuchi J. Measurement of large plane surface shapes by connecting small-aperture interferograms. Optical Engineering, 1994, 33(2): 608–613
CrossRef Google scholar
[214]
Murphy P, Forbes G, Fleig J, Stitching interferometry: A flexible solution for surface metrology. Optics and Photonics News, 2003, 14(5): 38–43
CrossRef Google scholar
[215]
Fleig J, Dumas P, Murphy P E, An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces. Proceedings of SPIE 5188, Advanced Characterization Techniques for Optics, Semiconductors, and Nanotechnologies, 2003, 5188: 296–307
CrossRef Google scholar
[216]
Dumas P R, Fleig J, Forbes G W, Flexible polishing and metrology solutions for free-form optics. In: Proceedings of the ASPE 2004 Winter Topical Meeting on Free-Form Optics: Design, Fabrication, Metrology, Assembly. Glasgow: Citeseer, 2004, 1–6
[217]
Lei Z, Liu X, Zhao L, A novel 3D stitching method for WLI based large range surface topography measurement. Optics Communications, 2016, 359: 435–447
CrossRef Google scholar
[218]
Niehaus F, Huttenhuis S, Danger T. New opportunities in freeform manufacturing using a long stroke fast tool system and integrated metrology. Proceedings of SPIE 9633, Optifab 2015, 2015, 9633: 96331E
[219]
Lei W, Hsu Y. Accuracy enhancement of five-axis CNC machines through real-time error compensation. International Journal of Machine Tools and Manufacture, 2003, 43(9): 871–877
CrossRef Google scholar
[220]
Yang J, Altintas Y. A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools. International Journal of Machine Tools and Manufacture, 2015, 88: 9–23
CrossRef Google scholar
[221]
Suh S H, Lee E S, Sohn J W. Enhancement of geometric accuracy via an intermediate geometrical feedback scheme. Journal of Manufacturing Systems, 1999, 18(1): 12–21
CrossRef Google scholar
[222]
Ke Z, Yuen A, Altintas Y. Pre-compensation of contour errors in five-axis CNC machine tools. International Journal of Machine Tools and Manufacture, 2013, 74(8): 1–11
CrossRef Google scholar
[223]
Gao W, Tano M, Sato S, On-machine measurement of a cylindrical surface with sinusoidal micro-structures by an optical slope sensor. Precision Engineering, 2006, 30(3): 274–279
CrossRef Google scholar
[224]
Gao W, Aoki J, Ju B F, Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine. Precision Engineering, 2007, 31(3): 304–309
CrossRef Google scholar
[225]
Gao W, Chen Y L, Lee K W, Precision tool setting for fabrication of a microstructure array. CIRP Annals-Manufacturing Technology, 2013, 62(1): 523–526
CrossRef Google scholar
[226]
Zou X, Zhao X, Li G, et al. Non-contact on-machine measurement using a chromatic confocal probe for an ultra-precision turning machine. International Journal of Advanced Manufacturing Technology, 2017, 90(5–8): 2163–2172
CrossRef Google scholar
[227]
Jiang X, Wang K, Martin H. Near common-path optical fiber interferometer for potentially fast on-line microscale-nanoscale surface measurement. Optics Letters, 2006, 31(24): 3603–3605
CrossRef Google scholar
[228]
Li D, Tong Z, Jiang X, Calibration of an interferometric on-machine probing system on an ultra-precision turning machine. Measurement, 2018, 118: 96–104
CrossRef Google scholar
[229]
Li D, Jiang X, Tong Z, Development and application of interferometric on-machine surface measurement for ultraprecision turning process. Journal of Manufacturing Science and Engineering, 2019, 141(1): 014502
CrossRef Google scholar
[230]
ElKott D F, Veldhuis S C. Isoparametric line sampling for the inspection planning of sculptured surfaces. Computer Aided Design, 2005, 37(2): 189–200
CrossRef Google scholar
[231]
He G, Sang Y, Pang K, An improved adaptive sampling strategy for freeform surface inspection on CMM. International Journal of Advanced Manufacturing Technology, 2018, 96(1–4): 1521–1535
CrossRef Google scholar
[232]
He G, Sang Y, Wang H, A profile error evaluation method for freeform surface measured by sweep scanning on CMM. Precision Engineering, 2019, 56: 280–292
CrossRef Google scholar
[233]
Babu M, Franciosa P, Ceglarek D. Adaptive measurement and modelling methodology for in-line 3D surface metrology scanners. Procedia CIRP, 2017, 60: 26–31
CrossRef Google scholar
[234]
Babu M, Franciosa P, Ceglarek D. Spatio-temporal adaptive sampling for effective coverage measurement planning during quality inspection of free form surfaces using robotic 3D optical scanner. Journal of Manufacturing Systems, 2019, 53: 93–108
CrossRef Google scholar
[235]
Chen Y, Peng C. Intelligent adaptive sampling guided by Gaussian process inference. Measurement Science & Technology, 2017, 28(10): 105005
CrossRef Google scholar
[236]
Yin Y, Ren M J, Sun L, Gaussian process based multi-scale modelling for precision measurement of complex surfaces. CIRP Annals-Manufacturing Technology, 2016, 65(1): 487–490
CrossRef Google scholar
[237]
Yin Y, Ren M J, Sun L. Dependant Gaussian processes regression for intelligent sampling of freeform and structured surfaces. CIRP Annals-Manufacturing Technology, 2017, 66(1): 511–514
CrossRef Google scholar
[238]
Gao W, Kemao Q. Parallel computing in experimental mechanics and optical measurement: A review. Optics and Lasers in Engineering, 2012, 50(4): 608–617
CrossRef Google scholar
[239]
Wang T, Kemao Q. Parallel computing in experimental mechanics and optical measurement: A review (II). Optics and Lasers in Engineering, 2018, 104: 181–191
CrossRef Google scholar
[240]
Karpinsky N, Zhang S. High-resolution, real-time 3D imaging with fringe analysis. Journal of Real-Time Image Processing, 2012, 7(1): 55–66
CrossRef Google scholar
[241]
Van der Jeught S, Soons J A, Dirckx J J. Real-time microscopic phase-shifting profilometry. Applied Optics, 2015, 54(15): 4953–4959
CrossRef Google scholar
[242]
Sinha A, Lee J, Li S, Lensless computational imaging through deep learning. Optica, 2017, 4(9): 1117–1125
CrossRef Google scholar
[243]
Rivenson Y, Göröcs Z, Günaydin H, Deep learning microscopy. Optica, 2017, 4(11): 1437–1443
CrossRef Google scholar
[244]
Rivenson Y, Zhang Y, Günaydın H, Phase recovery and holographic image reconstruction using deep learning in neural networks. Light, Science & Applications, 2018, 7(2): 17141
CrossRef Google scholar
[245]
Yin W, Chen Q, Feng S, Temporal phase unwrapping using deep learning. Scientific Reports, 2019, 9(1): 1–12
CrossRef Google scholar
[246]
Feng S, Zuo C, Yin W, Micro deep learning profilometry for high-speed 3D surface imaging. Optics and Lasers in Engineering, 2019, 121: 416–427
CrossRef Google scholar

Acknowledgements

This work received funding from the Enterprise Ireland and from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement (Grant No. 713654), the National Natural Science Foundation of China (Grant No. 51705070), and the Science Foundation Ireland (SFI) (Grant No. 15/RP/B3208). The authors appreciate the fruitful discussions and suggestions from Szymon Baron of DePuy Synthes. The authors would also like to thank Chengwei Kang of University College Dublin for his comments on the paper.

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