A Phase Retrieval Wavefront Detection Method for High Steepness Free-Form Surface

Abstract

The present invention discloses a phase recovery wavefront detection method for a high-steepness free-form surface. The method divides the free-form surface into multiple sub-areas, performs independent diffraction calculations on each sub-area, and replaces the whole-area diffraction calculations with the sub-area diffraction calculations, thereby reducing the amount of calculations for a single diffraction calculation. The wavefront is reconstructed using a phase recovery algorithm combined with the sub-area diffraction calculations to obtain the wavefront of the free-form surface to be measured, thereby realizing phase recovery wavefront detection for a high-steepness free-form surface. The present invention uses a sub-area diffraction calculation method to replace the traditional whole-area scalar diffraction calculation, so that the diffraction calculation results are more in line with the actual situation, improves the accuracy and robustness of the phase recovery wavefront detection technology, and improves the matching degree between the numerical model and the experimental model.

Description

Technical Field

[0001] The invention relates to the technical field of optical measurement, and in particular to a high-steepness free-form surface phase recovery wavefront detection method. Background Art

[0002] The measurement and analysis of light wavefront is one of the core research contents of modern adaptive optics, and is widely used in research fields such as quantitative phase microscopy and large-aperture optical component detection. The wavefront of light contains a lot of object information, such as the surface shape and internal structure of the object, atmospheric disturbances, biological structure, etc. Traditional wavefront detection methods are mainly divided into two categories: interference detection method and geometric ray method. Commonly used interferometers include Twyman-Green interferometer and Fizeau interferometer. However, the compensation lens in the interferometer is very expensive, has strict requirements on the detection environment, poor versatility, and very limited dynamic range. For high-steepness wavefront detection methods, the demodulation of the interferometer will be restricted by the resolution of the detector. There are many geometric ray methods, including Hartmann wavefront detection method, Shack–Hartmann wavefront detection method, Ronchi detection method, Moiré deflectometry, etc. Due to the process constraints of the microlens array, the accuracy of Hartmann detection and Shack–Hartmann detection methods is greatly affected by the sampling points in the detection system, and the spatial resolution of the recovered wavefront is also relatively low. The accuracy of moiré deflectometry is overly dependent on the quality of the grating. Although the Ronchi detection method can provide wavefront information, the wavefront can only detect the existence of low-order aberrations. Summary of the invention

[0003] Aiming at the disadvantages of traditional free-form surface shape detection methods, such as large amount of primary diffraction calculation, poor versatility, and limited dynamic range, the present invention proposes a high-steepness free-form surface phase recovery wavefront detection method. The specific technical scheme is as follows:

[0004] A high-steepness free-form surface phase recovery wavefront detection method, wherein a converging lens is arranged between a lens to be tested and an image sensor, and the image sensor is located at a defocused position of the converging lens;

[0005] The high-steepness free-form surface phase recovery wavefront detection method comprises the following steps:

[0006] S1: Set the aperture D and defocus distance Δz of the lens to be tested k , the total number of iterations of the phase recovery algorithm N_iter, the initial number of iterations i = 1;

[0007] S2: Obtain the target shape of the lens to be tested and divide it evenly into sub-areas, and calculate the complex amplitude wavefront G of the detector surface of the image sensor (5) based on the free-form surface diffraction calculation method and Fourier transform k ;

[0008]

[0009] Among them, |G k (u,v)| is G k The amplitude of G k The phase of; (u,v) is the coordinate in the frequency domain;

[0010] S3: The complex amplitude wavefront G k The amplitude in is replaced with the actual collected amplitude value to obtain the new light field distribution G k ';

[0011]

[0012] Among them, I det To collect the real amplitude value;

[0013] S4: distribute the new light field G k '(u,v) is transmitted back to the incident surface of the converging lens through the inverse Fourier transform to obtain the estimated value of the light field distribution on the incident surface g k '(x,y); where (x,y) is the spatial coordinate;

[0014] S5: g k The amplitude of '(x,y) is set to 1, constraining the light field of the incident surface of the converging lens, and obtaining the new light field g of the incident surface of the converging lens k+1 (x,y);

[0015] S6: i=i+1, return to S4, iterate N_iter times, reconstruct the incident surface wavefront of the converging lens, and obtain the wavefront error information of the lens to be tested.

[0016] Furthermore, the amplitude value I is actually collected in S4 det Obtained through:

[0017] The light intensity map of the wavefront error of the lens to be tested containing a free-form surface is collected, and the collected light intensity map is clipped using the centroid method to obtain I det .

[0018] Furthermore, the method for evenly dividing the shape in S3 to determine the center point is a breadth-first algorithm.

[0019] Furthermore, the free-form surface diffraction calculation method in S2 adopts a sub-aperture segmentation model, comprising the following steps:

[0020] S2.1: evenly divide the free-form surface into N_sub sub-areas, and obtain the shape of the free-form surface to be measured as z=g(x,y);

[0021] S2.2: Determine the positions of the inner sub-plane and the outer sub-plane corresponding to each sub-region; for the p-th sub-region, the positions of the inner sub-plane and the outer sub-plane are z=d1 and z=d2 respectively;

[0022]

[0023] S2.3: Set the refractive index of the lens to be tested to n, and the position of the front surface of the converging lens to z=d3;

[0024] S2.4: Parallel light is incident, and the wavefront expression of the internal sub-plane of the p-th sub-region is u p,1 ;

[0025] u p,1 =exp[jkd1]

[0026] Where k = 2π / λ;

[0027] S2.5: Eliminate the error caused by local curvature by phase compensation method and obtain the wavefront expression u of the external sub-plane of the p-th sub-region p, 2;

[0028]

[0029] in, is the phase compensation function, expressed as:

[0030]

[0031] rect(x,y) is used to limit the size of the sub-aperture, and its expression is as follows:

[0032]

[0033] S2.6: N_sub external sub-planes are diffracted to the front surface of the converging lens at position z=d3, and the diffraction fields are superimposed to obtain the angular spectrum field A at position z=d3:

[0034]

[0035] S2.7: Perform inverse Fourier transform on the angular spectrum field A to obtain the wavefront w of the free-form surface to be measured, which is expressed as follows:

[0036] w=∫Aexp(j2πux)exp(j2πvy)dudv.

[0037] A wavefront detection device for implementing the above method, the device comprises a laser transmitter, a beam expander, a lens to be measured, a converging lens and an image sensor, the beam expander is located behind the laser transmitter, the lens to be measured is located behind the beam expander, the converging lens is located behind the lens to be measured, and the image sensor is located behind the converging lens, the light source of the laser transmitter, the beam expander, the lens to be measured, the converging lens and the image sensor share a common optical axis, and the image sensor is located at a defocused position of the converging lens.

[0038] The beneficial effects of the present invention are as follows:

[0039] (1) The restored wavefront detection method of the present invention can be applied to lenses to be tested with different free-form surfaces, and can improve the accuracy of wavefront detection and the matching degree with the experimental model.

[0040] (2) The present invention adopts a sub-aperture segmentation model, which divides the free-form surface into multiple sub-regions, performs independent diffraction calculations on each sub-region, and replaces the entire region diffraction calculation with the sub-region diffraction calculation, thereby reducing the amount of calculation for a single diffraction calculation. On this basis, the present invention further uses the phase compensation method to compensate for local errors, thereby making the diffraction calculation results more consistent with the actual situation, improving the accuracy and robustness of the phase recovery wavefront detection technology, and improving the matching degree between the numerical model and the experimental model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a schematic diagram of the structure of a high-steepness free-form surface phase recovery wavefront detection device.

[0042] Figure 2 The flowchart of the high-steepness free-form surface phase recovery wavefront detection method of the present invention.

[0043] Figure 3 It is a detection result diagram of the high-steepness free-form surface phase recovery wavefront detection method of the present invention, wherein the left figure represents the real wavefront, the middle figure is the reconstructed wavefront diagram proposed by the present invention, and the right figure is the detection result diagram of the traditional GS algorithm. DETAILED DESCRIPTION

[0044] The present invention will be described in detail below based on the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become more clear. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0045] like Figure 1As shown, the high-steepness free-form surface phase recovery wavefront detection device of the present invention comprises a laser emitter 1, a beam expander 2, a lens to be measured 3, a converging lens 4 and an image sensor 5. The beam expander 2 is located after the laser emitter 1, the lens to be measured 3 is located after the beam expander 2, the converging lens 4 is located after the lens to be measured 3, and the image sensor 5 is located after the converging lens 4. The light source of the laser emitter 1, the beam expander 2, the lens to be measured 3, the converging lens 4 and the image sensor 5 are on the same optical axis, and the image sensor 5 is located at the defocus position of the converging lens 4.

[0046] The wavefront detection device of the present invention collects a light intensity map containing the wavefront error of the free-form surface lens to be measured, and the collected light intensity map is cut to obtain a two-dimensional intensity map I det As one of the cropping methods, the centroid method is preferably used for cropping.

[0047] like Figure 2 As shown, the high-steepness free-form surface phase recovery wavefront detection method of the present invention comprises the following steps:

[0048] S1: Set the aperture D and defocus distance Δz of the lens to be tested k , the total number of iterations of the phase recovery algorithm N_iter, the initial number of iterations i = 1;

[0049] S2: Obtain the target shape of the lens to be tested and divide it evenly into sub-areas, and calculate the complex amplitude wavefront G of the detector surface of the image sensor 5 based on the free-form surface diffraction calculation method and Fourier transform k ;

[0050]

[0051] Among them, |G k (u,v)| is G k The amplitude of G k The phase of ; (u,v) is the coordinate in the frequency domain.

[0052] Preferably, a breadth-first algorithm is used to evenly divide the target shape of the lens to be tested to determine the center point. S2 specifically includes the following sub-steps:

[0053] S2.1: evenly divide the free-form surface into N_sub sub-areas, and obtain the shape of the free-form surface to be measured as z=g(x,y);

[0054] S2.2: Determine the positions of the inner sub-plane and the outer sub-plane corresponding to each sub-region; for the p-th sub-region, the positions of the inner sub-plane and the outer sub-plane are z=d1 and z=d2 respectively;

[0055]

[0056] S2.3: Set the refractive index of the lens to be tested to n, and the position of the front surface of the converging lens to z=d3;

[0057] S2.4: Parallel light is incident, and the wavefront expression of the internal sub-plane of the p-th sub-region is u p, 1 ;

[0058] u p,1 =exp[jkd1]

[0059] Where k = 2π / λ;

[0060] S2.5: Eliminate the error caused by local curvature by phase compensation method and obtain the wavefront expression u of the external sub-plane of the p-th sub-region p, 2;

[0061]

[0062] in, is the phase compensation function, expressed as:

[0063]

[0064] rect(x,y) is used to limit the size of the sub-aperture, and its expression is as follows:

[0065]

[0066] S2.6: N_sub external sub-planes are diffracted to the front surface of the converging lens at position z=d3, and the diffraction fields are superimposed to obtain the angular spectrum field A at position z=d3:

[0067]

[0068] S2.7: Perform inverse Fourier transform on the angular spectrum field A to obtain the wavefront w of the free-form surface to be measured, which is expressed as follows:

[0069] w=∫Aexp(j2πux)exp(j2πvy)dudv.

[0070] S3: The complex amplitude wavefront G k The amplitude in is replaced with the actual collected amplitude value to obtain the new light field distribution G k ';

[0071]

[0072] S4: distribute the new light field G k '(u,v) is transmitted back to the incident surface of the converging lens through the inverse Fourier transform to obtain the estimated value of the light field distribution on the incident surface g k'(x,y); where (x,y) is the spatial coordinate;

[0073] S5: g k The amplitude of '(x,y) is set to 1, constraining the light field of the incident surface of the converging lens, and obtaining the new light field g of the incident surface of the converging lens k+1 (x,y);

[0074] S6: Return to S4, i=i+1, iterate N_iter times, reconstruct the incident surface wavefront of the converging lens, and obtain the wavefront error information of the lens to be tested.

[0075] A specific embodiment of the method of the present invention is given below to illustrate the technical effect of the method.

[0076] Here, the focal length of the converging lens is selected to be 180 mm, the test wavelength is 546.1 nm, the total number of iterations of wavefront detection is 500, and the number of effective spot sampling is 4096×4096.

[0077] In this embodiment, the defocused diffraction image is collected to reconstruct the phase and amplitude of the wavefront, and the free-form surface diffraction calculation method selected is based on the sub-aperture segmentation model. Figure 3 The figure is the restoration result of the method proposed in the present invention. The left figure shows the real wavefront, the middle figure shows the reconstructed wavefront proposed in the present invention, and the right figure shows the detection result of the traditional GS algorithm. The effectiveness of the method proposed in the present invention can be seen from the figure.

[0078] Those skilled in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the above examples, those skilled in the art can still modify the technical solutions recorded in the above examples or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, etc. made within the spirit and principle of the invention shall be included in the protection scope of the invention.

Claims

1. A high-steepness free-form surface phase recovery wavefront detection method, characterized in that: A converging lens (4) is arranged between the lens to be tested (4) and the image sensor (5), and the image sensor (5) is located at a defocused position of the converging lens (4); The high-steepness free-form surface phase recovery wavefront detection method comprises the following steps: S1: Set the aperture D and defocus distance Δz of the lens to be tested k , the total number of iterations of the phase recovery algorithm N_iter, the initial number of iterations i = 1; S2: Obtain the target shape of the lens to be tested and divide it evenly into sub-areas, and calculate the complex amplitude wavefront G of the detector surface of the image sensor (5) based on the free-form surface diffraction calculation method and Fourier transform k ; Among them, |G k (u,v)| is G k The amplitude of G k The phase of; (u, v) is the coordinate in the frequency domain; S3: The complex amplitude wavefront G k The amplitude in is replaced with the actual collected amplitude value to obtain the new light field distribution G k '; Among them, I det To collect the real amplitude value; S4: distribute the new light field G k '(u,v) is transmitted back to the incident surface of the converging lens through the inverse Fourier transform to obtain the estimated value of the light field distribution on the incident surface g k '(x,y); where (x,y) is the spatial coordinate; S5: g k The amplitude of '(x,y) is set to 1, constraining the light field of the incident surface of the converging lens, and obtaining the new light field g of the incident surface of the converging lens k+1 (x,y); S6: i=i+1, return to S4, iterate N_iter times, reconstruct the incident surface wavefront of the converging lens, and obtain the wavefront error information of the lens to be tested; The free-form surface diffraction calculation method in S2 adopts a sub-aperture segmentation model and includes the following steps: S2.1: evenly divide the free-form surface into N_sub sub-areas, and obtain the shape of the free-form surface to be measured as z=g(x,y); S2.2: Determine the positions of the inner sub-plane and the outer sub-plane corresponding to each sub-region; for the p-th sub-region, the positions of the inner sub-plane and the outer sub-plane are z=d1 and z=d2 respectively; S2.3: Set the refractive index of the lens to be tested to n, and the position of the front surface of the converging lens to z=d3; S2.4: Parallel light is incident, and the wavefront expression of the internal sub-plane of the p-th sub-region is u p,1 ; in p,1 =exp[jkd1] Where k = 2π / λ; S2.5: Eliminate the error caused by local curvature by phase compensation method and obtain the wavefront expression u of the external sub-plane of the p-th sub-region p,2 ; in, is the phase compensation function, expressed as: rect(x,y) is used to limit the size of the sub-aperture, and its expression is as follows: S2.6: N_sub external sub-planes are diffracted to the front surface of the converging lens at position z=d3, and the diffraction fields are superimposed to obtain the angular spectrum field A at position z=d3: S2.7: Perform inverse Fourier transform on the angular spectrum field A to obtain the wavefront w of the free-form surface to be measured, which is expressed as follows: w=∫Aexp(j2πux)exp(j2πvy)dudv.

2. The high-steepness free-form surface phase recovery wavefront detection method according to claim 1, characterized in that: The amplitude value I is actually collected in S3 det Obtained through: The light intensity map of the wavefront error of the lens to be tested containing a free-form surface is collected, and the collected light intensity map is clipped using the centroid method to obtain I det .

3. The high-steepness free-form surface phase recovery wavefront detection method according to claim 1, characterized in that: The method for evenly dividing the shape in S2 to determine the center point is a breadth-first algorithm.

4. A wavefront detection device for implementing the method of any one of claims 1 to 3, characterized in that: The device comprises a laser emitter (1), a beam expander (2), a lens to be measured (3), a converging lens (4) and an image sensor (5); the beam expander (2) is located behind the laser emitter (1); the lens to be measured (3) is located behind the beam expander (2); the converging lens (4) is located behind the lens to be measured (3); the image sensor (5) is located behind the converging lens (4); the light source of the laser emitter (1), the beam expander (2), the lens to be measured (3), the converging lens (4) and the image sensor (5) share a common optical axis, and the image sensor (5) is located at a defocused position of the converging lens (4).

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