CN107576403B - Phase recovery device based on Talbot effect and its working method - Google Patents

Abstract

A phase recovery device based on the Ronchi grating Talbot effect and a working method thereof are composed of a Ronchi grating and a high-sensitivity CCD camera and are characterized in that the CCD camera is located at the Talbot distance of the Ronchi grating th step, Ronchi grating self-imaging is obtained through the CCD camera, the obtained Ronchi grating self-imaging is preprocessed for removing background noise and the like, the phase recovery is carried out, phase information is optimized through multiple cycle iteration of a phase recovery algorithm, and finally incident wavefront is optimized and output.

Description

Phase recovery device based on Talbot effect and its working method

technical field

The invention belongs to the field of optical technology and relates to a novel phase recovery technology, in particular to a phase recovery device based on the Talbot effect of a Ronchi grating and a working method of the device. This technology can be used to achieve high-precision phase measurement, wavefront analysis, and optical system inspection.

Background technique

Phase recovery technology is a technology that recovers incident phase information by measuring light field intensity information. It has the characteristics of high precision and high sensitivity, and has a wide range of fields such as electron microscopy imaging, phase measurement, wavefront analysis and image encryption. application.

Phase recovery was first proposed by R.W.Gerchberg and W.O.Saxton in 1972. This algorithm uses the light field intensity information of the exit pupil surface and the image plane to iteratively restore the phase information of the light field at the exit pupil surface. This algorithm is the phase recovery algorithm. The beginning of - the GS algorithm. The phase recovery algorithm is the core of the phase recovery technology. The convergence characteristics of the algorithm are the key factors for the success or failure of the phase recovery technology. Although the GS algorithm has high recovery accuracy, the GS algorithm relies on multi-faceted intensity measurement, and there are problems of slow convergence speed or even non-convergence and iteration. Problems such as many times. Based on the GS algorithm, many improved algorithms have also been proposed. Based on the GS algorithm, the hybrid input-output algorithm (HIO) strengthens the constraints and improves the convergence speed, and is mostly used in coherent diffraction imaging. However, the HIO algorithm has many local minima problems and cannot always converge to the correct value; using The light intensity information of three or more planes or the method of using multi-wavelength light sources to collect diffraction patterns for phase recovery has also achieved good convergence results, but the disadvantages are high system complexity and cumbersome operations, which reduce the efficiency of the algorithm.

SUMMARY OF THE INVENTION

In order to overcome the above-mentioned deficiencies of the existing phase recovery technology, the purpose of the present invention is to provide a device for recovering the phase by using the stochastic parallel gradient descent algorithm based on the Talbot effect of the Ronchi grating, and a working method of the device. The optical path structure of the solution is simple, easy to implement, convenient for image acquisition, and capable of realizing fast and high-precision phase recovery.

In order to achieve the above object, the technical solution adopted in the present invention is: a phase recovery device based on the Talbot effect of the Ronchi grating, the device uses the Ronchi grating and a high-sensitivity CCD camera, and is characterized in that the CCD camera is located in the Ronchi grating. at the Talbot distance.

The Talbot effect is a phenomenon in which the periodic structure self-imaging occurs at some specific distances in the rear Fresnel diffraction region of a periodic structure object under the vertical illumination of a monochromatic plane wave. The CCD camera is placed in the Fresnel diffraction area directly behind the Ronchi grating, and the self-imaging of the grating will be detected at the Talbot distance of the Ronchi grating. The intensity distribution of the self-imaging is consistent with the structure of the Ronchi grating. If the position of the CCD camera is deviated from the Talbot distance, the detected image cannot be self-imaging or the contrast is reduced, which is not conducive to the subsequent phase recovery.

The specific position of "the CCD camera is located at the Talbot distance of the Ronchi grating" is determined according to the following formula:

Talbot distance formula for Ronchi grating:

m取正整数，d为Ronchi光栅的周期，λ为入射光波长。Among them, L represents the propagation distance of light along the optical axis after passing through the Ronchi grating, and its size is

m is a positive integer, d is the period of the Ronchi grating, and λ is the wavelength of the incident light.

"The CCD camera is located at the Talbot distance of the Ronchi grating" can also be described as: "The CCD camera is located at the rear surface Z _T of the Ronchi grating" is a different statement of the same meaning.

When in use, the present invention forms an analysis system in the following manner: on the same optical axis, the Ronchi grating and the CCD camera are placed in sequence. Among them, the CCD camera is placed at the Talbot distance from the rear surface of the Ronchi grating.

The principle of the present invention is as follows: the Ronchi grating is used for diffraction imaging of the vertically incident wavefront, the high-sensitivity CCD camera is used to record its self-imaging intensity information at the Talbot distance of the Ronchi grating, and the phase information of the incident wavefront is obtained through a phase recovery algorithm. A schematic diagram of the structure of the present invention is shown in FIG. 1 . The hardware implementation of the present invention is very similar to the traditional Shack-Hartmann wavefront sensor, the difference is that the Shack-Hartmann sensor uses a microlens array to image the incident wavefront geometry, and the present invention uses a Ronchi grating to image the incident wavefront diffraction; the Shack-Hartmann wavefront sensor Differential calculation is used to recover the wavefront information by measuring the centroid offset, while the present invention adopts a stochastic parallel gradient descent phase recovery algorithm.

The technical solution for accomplishing the second invention task of the present application is a phase recovery method based on the Talbot effect of a Ronchi grating using the above device, characterized in that the steps are as follows:

The first step is to obtain the Ronchi grating self-imaging through the CCD camera;

The second step is to perform preprocessing such as removing background noise on the obtained Ronchi grating self-imaging;

In the third step, phase recovery is performed, and the phase information is optimized through multiple iterations of the stochastic parallel gradient descent algorithm, and finally the output incident wavefront is optimized.

It should be noted that the Ronchi grating used in the present invention is an amplitude transmission grating with a grating duty cycle of 0.5. The selection of the period d of the Ronchi grating has a great influence on the phase recovery performance of the present invention. Although the current manufacturing process can produce gratings with thousands of line pairs per millimeter, under the condition of the same incident wavelength, the Talbot distance corresponding to a too small grating period is too small, and the requirement for CCD position accuracy is too high, which is not conducive to The actual operation increases the detection difficulty of the CCD camera; the larger the grating period is, the larger the corresponding Talbot distance is. Due to the influence of the limited aperture diffraction of the incident wave, the detected intensity image is more blurred and the detection dynamic range is smaller.

公式中的m取1；适当的光栅周期为100μm左右。It is recommended in the present invention that the Talbot distance should be double the Talbot distance, that is,

The m in the formula is taken as 1; the appropriate grating period is about 100μm.

The description of wavefront aberration adopts the commonly used Zernike polynomial representation, and the incident wavefront phase can be described as a linear combination of Zernike polynomials:

Among them, j is the number of terms of the Zernike polynomial, φ(x, y) is the phase of the incident wavefront, and the first term of the Zernike polynomial does not affect the imaging quality and can be ignored. During phase recovery, the light intensity distribution information actually obtained by the CCD camera is I(x,y). Assuming that the phase of the incident wavefront is linearly combined by the Zernike polynomial, the intensity distribution on the plane where the CCD camera is located can be theoretically calculated |U(x ,y)| ² . Therefore, the evaluation function of the phase optimization algorithm is defined as:

Among them, where I(x _i , y _j ) is the intensity value of the pixel point (i, j) in the self-imaging measured by the CCD camera, and k is the number of iterations. It can be seen that when the value of the evaluation function gradually decreases and approaches a small value, the phase information of the incident wavefront can be obtained. The phase recovery flowchart is shown in Figure 2.

An example of a theoretical simulation model of phase recovery is shown in Figure 3. Figure 3(a) is the input phase, (b) is the self-imaging intensity distribution of the Ronchi grating Talbot, (c) is the recovered phase, (d) is the residual between the input phase and the recovered phase, (e)-(g) Corresponding to (b)-(d), respectively, the input phase is unchanged, only Gaussian noise is introduced, and the simulation results in the case of a signal-to-noise ratio of 5. It can be seen that the PV value of the input phase is about 1 wavelength, and the residual difference between the recovered phase and the input phase is on the order of 10 ^-3 . Figure 4 shows the comparison results of the Zernike coefficients corresponding to the phases (a), (c), and (f) in Figure 3. It can be seen that the Zernike coefficients of the restored phase before and after adding noise are basically the same as the Zernike coefficients of the input phase, and the difference is very large. is small, indicating that the present invention can be used to realize fast and high-precision phase recovery, and has strong anti-noise capability.

Compared with the existing phase recovery technology, the present invention mainly has the following advantages:

(1) The system structure of the present invention is simple and easy to implement. The present invention utilizes the Talbot effect of the Ronchi grating—lensless diffraction imaging, and the system structure is simple and easy to build. It only needs to use a CCD camera to perform a single intensity image acquisition on the Talbot plane, avoiding the tedious multi-faceted intensity image acquisition process in other phase recovery methods. .

(2) The present invention has fast phase recovery speed and high precision. Based on the self-imaging intensity information of the Ronchi grating, a stochastic parallel gradient descent optimization algorithm is used to recover the phase information, which has fast convergence speed and high precision.

(3) The present invention has strong anti-noise ability. Different from the traditional Shack-Hartmann wavefront sensor, which uses the centroid offset to obtain the wavefront information through differential operation, the present invention is a phase recovery optimization algorithm, which is not sensitive to noise, and can still obtain the wavefront information under the condition of low signal-to-noise ratio. Better phase recovery results.

Description of drawings

Fig. 1 Schematic diagram of the system structure of the phase recovery technology based on the Talbot effect of the Ronchi grating. Among them, 1-1 is a Ronchi grating, and 1-2 is a high-sensitivity CCD camera.

Figure 2 is a flow chart of the phase recovery technique based on the Talbot effect of the Ronchi grating.

Fig. 3 Theoretical simulation example of the phase recovery technique based on the Talbot effect of the Ronchi grating.

Fig. 4 Comparison of Zernike coefficients of theoretical simulation examples of phase recovery technology based on Ronchi grating Talbot effect.

Detailed ways

Embodiment 1, the phase recovery technology based on the Talbot effect of the Ronchi grating, referring to FIG. 1, the realization of the present invention is completed by the Ronchi grating and the high-resolution CCD camera, the CCD cameras 1-2 are located at the Talbot distance of the Ronchi grating, and the technical implementation steps As follows: the first step is to obtain the Ronchi grating self-imaging through the CCD camera; the second step is to perform preprocessing such as background noise removal on the obtained Ronchi grating self-image; The loop iteratively optimizes the phase information, and finally optimizes the output incident wavefront. The specific position of "the CCD camera is located at the Talbot distance of the Ronchi grating" is determined according to the following formula:

Talbot distance formula for Ronchi grating:

m取正整数，d为Ronchi光栅的周期，λ为入射光波长。Among them, L represents the propagation distance of light along the optical axis after passing through the Ronchi grating, and its size is

m is a positive integer, d is the period of the Ronchi grating, and λ is the wavelength of the incident light.

The steps of the phase recovery method based on the Ronchi grating Talbot effect using the above device are as follows:

The first step is to obtain the Ronchi grating self-imaging through the CCD camera;

The second step is to perform preprocessing such as removing background noise on the obtained Ronchi grating self-imaging;

In the third step, phase recovery is performed, and the phase information is optimized through multiple iterations of the stochastic parallel gradient descent algorithm, and finally the output incident wavefront is optimized.

Claims (4)

1. a phase recovery method based on Ronchi grating Talbot effect, is characterized in that, step is as follows: The first step is to obtain the Ronchi grating self-imaging through the CCD camera; The second step is to preprocess the acquired Ronchi grating self-imaging to remove background noise; The third step is to perform phase recovery, optimize the phase information through multiple iterations of the stochastic parallel gradient descent algorithm, and finally optimize the output incident wavefront; The phase recovery algorithm in the third step adopts the stochastic parallel gradient descent optimization algorithm; The optimized output incident wavefront described in the third step, wherein the wavefront aberration is characterized by a linear combination of Zernike polynomials:

Among them, j is the number of terms of the Zernike polynomial, and φ(x, y) is the phase of the incident wavefront; In the optimized output incident wavefront described in the third step, the light intensity distribution information actually obtained by the CCD camera is I(x,y); through the assumed wavefront, the intensity of the plane where the CCD camera is located is obtained through theoretical calculation distribution |U(x,y)| ² ; accordingly, the evaluation function of the phase optimization algorithm is defined as: EF=∑ _i,j |I( _xi ,y _j )-|U _k ( _xi ,y _j )| ² | ² , Among them, where I(x _i , y _j ) is the intensity value of the pixel point (i, j) in the self-imaging measured by the CCD camera, and k is the number of iterations; The equipment used for this method is: A phase recovery device based on the Talbot effect of the Ronchi grating, which uses a Ronchi grating and a high-sensitivity CCD camera, and the CCD camera is located at the Talbot distance of the Ronchi grating; The specific position of "the CCD camera is located at the Talbot distance of the Ronchi grating" is determined according to the following formula: Talbot distance formula for Ronchi grating: Among them, L represents the propagation distance of light along the optical axis after passing through the Ronchi grating, and its size is

m is a positive integer, d is the period of the Ronchi grating, and λ is the wavelength of the incident light. 2. the phase recovery method based on Ronchi grating Talbot effect according to claim 1 is characterized in that, when in use, this device forms an analysis system as follows: on the same optical axis, place Ronchi grating, CCD camera successively, Among them, the CCD camera was placed at Talbot distance from the rear surface of the Ronchi grating. 3 . The phase recovery method based on the Talbot effect of a Ronchi grating according to claim 1 or 2 , wherein the Ronchi grating is an amplitude transmission grating, and the duty ratio of the grating is 0.5. 4 . 4. the phase recovery method based on Ronchi grating Talbot effect according to claim 3, is characterized in that, described Talbot distance chooses one time Talbot distance:

In the formula, m is taken as 1; the grating period is 100 μm.

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