CN107576403B

CN107576403B - Phase recovery device based on Talbot effect and working method thereof

Info

Publication number: CN107576403B
Application number: CN201710730789.XA
Authority: CN
Inventors: 李常伟; 张思炯; 陈升
Original assignee: Nanjing Institute of Astronomical Optics and Technology NIAOT of CAS
Current assignee: Nanjing Institute of Astronomical Optics and Technology NIAOT of CAS
Priority date: 2017-07-28
Filing date: 2017-08-23
Publication date: 2020-01-31
Anticipated expiration: 2037-08-23
Also published as: CN107576403A

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 working method thereof

Technical Field

The invention belongs to the technical field of optics, relates to novel phase recovery technologies, and particularly relates to phase recovery devices based on the Ronchi grating Talbot effect and a working method of the devices.

Background

The phase recovery technology is technologies for recovering incident phase information by measuring light field intensity information, has the characteristics of high precision and high sensitivity, and has -wide application in the fields of electron microscopic imaging, phase measurement, wavefront analysis, image encryption and the like.

Phase recovery was first proposed in 1972 by r.w. gerchberg and w.o.saxton, which iteratively recovers the phase information of the exit pupil plane lightfield using the lightfield intensity information of both the exit pupil plane and the image plane, which is the beginning of the phase recovery algorithm, the GS algorithm. The phase recovery algorithm is the core of the phase recovery technology, the convergence characteristic of the algorithm is a key factor of success or failure of the phase recovery technology, and the GS algorithm has high recovery precision, but depends on multi-surface strength measurement, and has the problems of low convergence speed, even no convergence, multiple iteration times and the like. Based on the GS algorithm, many improved algorithms have also been proposed in succession. The hybrid input and output algorithm (HIO) strengthens constraint conditions on the basis of the GS algorithm, improves convergence speed, is mainly used in coherent diffraction imaging, but has the problems of a plurality of local minimum values and can not always converge to a correct value; the method of collecting diffraction patterns for phase recovery by using light intensity information of three or more surfaces or using a multi-wavelength light source also obtains good convergence effect, but has the defects of high system complexity, complex operation and reduced algorithm efficiency.

Disclosure of Invention

In order to overcome the defects of the existing phase recovery technology, the invention aims to provide devices for recovering the phase by using a random parallel gradient descent algorithm based on the Talbot effect of the Ronchi grating and a working method of the devices.

In order to achieve the purpose, the invention adopts the technical scheme that phase recovery devices based on the Ronchi grating Talbot effect use Ronchi gratings and high-sensitivity CCD cameras, and are characterized in that the CCD cameras are positioned at the Talbot distance of the Ronchi gratings.

The Talbot effect is a phenomenon that self-imaging of periodic structure objects occurs at specific distances in a rear Fresnel diffraction zone of the periodic structure objects under the condition that monochromatic plane waves are vertically irradiated, a CCD camera is arranged in the Fresnel diffraction zone right behind a Ronchi grating, self-imaging of the grating is detected at the Talbot distance of the Ronchi grating, the intensity distribution of the self-imaging is kept with the structure of the Ronchi grating, if the CCD camera is arranged at a position deviating from the Talbot distance, the detected image cannot be self-imaged or the contrast is reduced, and subsequent phase recovery is not facilitated.

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

the Talbot distance formula for Ronchi gratings:

wherein L represents the propagation distance of light passing through the Ronchi grating along the optical axis, and has a value of

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: distance Ronchi grating rear surface Z of CCD camera_TWhere "is a different statement with the same meaning.

In use, the present invention comprises an analysis system comprising a Ronchi grating, a CCD camera placed in sequence on the same optical axis as , wherein the CCD camera is placed at a Talbot distance from the rear surface of the Ronchi grating.

The principle of the invention is as follows: utilizing the Ronchi grating to perform diffraction imaging on a vertically incident wave surface, using a high-sensitivity CCD camera to record self-imaging intensity information of the Ronchi grating at the Talbot distance, and obtaining phase information of the incident wave surface through a phase recovery algorithm. The structure of the invention is schematically shown in figure 1. The hardware implementation of the invention is very similar to the traditional Shack-Hartmann wavefront sensor, and the difference is that the incident wave surface is geometrically imaged by using a micro-lens array in the Shack-Hartmann sensor, and the incident wave surface is imaged by diffraction by using a Ronchi grating; the Shack-Hartmann wavefront sensor recovers wavefront information using differential calculations by measuring centroid shifts, while the present invention employs a random parallel gradient descent phase recovery algorithm.

The technical solution for accomplishing the second invention task of the present application is phase recovery methods based on the Ronchi grating Talbot effect using the above-mentioned device, characterized by the following steps:

, obtaining Ronchi grating self-imaging through a CCD camera;

secondly, preprocessing the obtained Ronchi grating self-imaging such as removing background noise;

and thirdly, phase recovery is carried out, phase information is optimized through multiple times of circulating iteration of a random parallel gradient descent algorithm, and finally the incident wavefront is optimized and output.

Although the prior manufacturing process can produce gratings reaching thousands of line pairs per millimeter, under the condition of the same incident wavelength of , the Talbot distance corresponding to the too small grating period is too small, the requirement on the position precision of the CCD is too high, the actual operation is not facilitated, and the detection difficulty of the CCD camera is increased.

According to the recommendation of the invention, selecting the Talbot distance to be times of the Talbot distance, namely

M in the formula is 1; a suitable grating period is around 100 μm.

The wavefront aberration is described using commonly used Zernike polynomial expressions, and the incident wavefront phase can be described as a linear combination of Zernike polynomials:

wherein j is the number of terms of the Zernike polynomial, phi (x, y) is the incident wavefront phase, the th term of the Zernike polynomial does not affect the imaging quality and can not be considered, during phase recovery, the light intensity distribution information actually obtained by the CCD camera is I (x, y), the incident wavefront phase is assumed to be formed by linear combination of the Zernike polynomials, and the intensity distribution | U (x, y) <' > of the plane where the CCD camera is located can be theoretically calculated². Thus, the merit function defining the phase optimization algorithm is:

wherein I (x)_i,y_j) The value is the intensity value of the pixel point (i, j) in the self-imaging measured by the CCD camera, and k is the iteration number. Therefore, when the evaluation function value is gradually reduced and approaches to a certain small value, the incident wavefront phase information can be obtained. The phase recovery flow chart is shown in fig. 2.

FIG. 3 shows theoretical simulation model examples of phase recovery, FIG. 3(a) shows the input phase, (b) shows the Ronchi grating Talbot self-imaging intensity distribution, (c) shows the recovered phase, (d) shows the residual error between the input phase and the recovered phase, and (e) - (g) correspond to (b) - (d), respectively, and show the simulation results of the case where the input phase is unchanged, only Gaussian noise is introduced, and the signal-to-noise ratio is 5^-3Figure 4 is the result of comparing the Zernike coefficients corresponding to the phases (a), (c) and (f) in figure 3, and it can be seen that the Zernike coefficients of the recovered phases before and after adding noise and the Zernike coefficients of the input phases are basically maintained , and the difference is very small, which shows that the invention can be used for realizing fast and high-precision phase recovery and has strong anti-noise capability.

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

(1) the system of the invention has simple structure and is easy to realize. The method utilizes the Talbot effect of the Ronchi grating, namely lens-free diffraction imaging, has simple and easily-built system structure, only needs to use a CCD camera to carry out single-time intensity image acquisition on the Talbot plane, and avoids the complicated multi-surface intensity image acquisition process in other phase recovery methods.

(2) The invention has fast phase recovery speed and high precision. Based on the self-imaging intensity information of the Ronchi grating, the phase information is recovered by adopting a random parallel gradient descent optimization algorithm, and the algorithm has high convergence speed and high precision.

(3) The invention has strong anti-noise capability, is different from the traditional Shack-Hartmann wavefront sensor which obtains wavefront information by using centroid offset through differential operation, is the phase recovery optimization algorithm, is insensitive to noise, and can still obtain a better phase recovery result under the condition of low signal-to-noise ratio.

Drawings

Fig. 1 is a schematic structural diagram of a system of a phase recovery technology based on the wavelength grating Talbot effect. Wherein, 1-1 is Ronchi grating, and 1-2 is high-sensitivity CCD camera.

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

Fig. 3 is an example of a theoretical simulation of a phase recovery technique based on the pencil grating Talbot effect.

Figure 4 Zernike coefficient contrast for a theoretical simulation example of a phase recovery technique based on the Ronchi grating Talbot effect.

Detailed Description

Embodiment 1, a phase recovery technology based on the Talbot effect of a Ronchi grating, referring to fig. 1, the implementation of the invention is completed by a Ronchi grating and a high-resolution CCD camera, and the CCD camera 1-2 is located at the Talbot distance of the Ronchi grating, the technology implementation steps are , obtaining the self-imaging of the Ronchi grating through the CCD camera, the second, removing background noise and other preprocessing to the obtained self-imaging of the Ronchi grating, the third, performing phase recovery, optimizing phase information through multiple circulation iterations by a random parallel gradient descent algorithm, and finally optimizing and outputting an incident wavefront, wherein the specific position of the CCD camera located at the Talbot distance of the Ronchi grating is determined according to the following formula:

the Talbot distance formula for Ronchi gratings:

The method for phase recovery based on the Ronchi grating Talbot effect by adopting the device comprises the following steps:

, obtaining Ronchi grating self-imaging through a CCD camera;

Claims

1, phase recovery methods based on the Ronchi grating Talbot effect, which is characterized by the following steps:

, obtaining Ronchi grating self-imaging through a CCD camera;

secondly, carrying out background noise removal pretreatment on the obtained Ronchi grating self-imaging;

thirdly, phase recovery is carried out, phase information is optimized through multiple times of cyclic iteration of a random parallel gradient descent algorithm, and finally the incident wavefront is optimized and output;

in the third step, a phase recovery algorithm adopts a random parallel gradient descent optimization algorithm;

and the third step of optimizing and outputting the incident wavefront, wherein the wavefront aberration is characterized by adopting a Zernike polynomial linear combination:

wherein j is the term of Zernike polynomial and phi (x, y) is the incident wavefront phase;

the third step is to optimize the output of the incident wavefront, wherein the light intensity distribution information actually obtained by the CCD camera is I (x, y); calculating the intensity distribution | U (x, y) & lt Y & gt of the plane where the CCD camera is located by theory through the assumed wave front²(ii) a Accordingly, the evaluation function defining the phase optimization algorithm is:

EF＝∑_i,j|I(x_i,y_j)-|U_k(x_i,y_j)|²|²，

wherein I (x)_i,y_j) The value is the intensity value of the pixel point (i, j) in the self-imaging measured by the CCD camera, and k is the iteration number;

the equipment used by the method is as follows:

a phase recovery device based on the Talbot effect of a Ronchi grating uses the Ronchi grating and a high-sensitivity CCD camera, and the CCD camera is positioned at the Talbot distance of the Ronchi grating;

the Talbot distance formula for Ronchi gratings:

2. The method for phase recovery based on the Talbot effect of the Ronchi grating as claimed in claim 1, wherein the device comprises an analysis system in such a way that the Ronchi grating and the CCD camera are sequentially placed on the same optical axis, wherein the CCD camera is placed at the Talbot distance from the rear surface of the Ronchi grating.

3. The method for phase recovery based on the Ronchi grating Talbot effect according to claim 1 or 2, wherein the Ronchi grating is an amplitude type transmission grating, and the grating duty cycle is 0.5.

4. The method for phase recovery based on the Ronchi grating Talbot effect of claim 3, wherein the Talb is derived from the grating of the Ronchi gratingSelecting the ot distance to be times of the Talbot distance:

m in the formula is 1; the grating period is 100 μm.