CN115131233A - Intensity background light suppression method for computational imaging - Google Patents
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Abstract
The invention discloses an intensity background light suppression method for computational imaging, which comprises the steps of firstly, simulating an actual optical system through mathematical modeling to obtain the size of a diffraction spot area with a high signal-to-noise ratio, and further establishing a support domain for establishing a background light model; and secondly, re-segmenting the polynomial according to the background light support domain, fitting and representing the background light outside the background light support domain to obtain a coefficient, combining the unsegmented polynomial and the coefficient to fit and represent the background light of the full-spot image, and removing the background light from the acquired intensity. According to the invention, the support domain outside the light spot is obtained through mathematical modeling, and the suppression and removal of the background light are realized based on the polynomial, so that the image acquisition process of the computed imaging is simplified, the application range of the computed imaging is expanded, and the accuracy of wavefront reconstruction is improved.
Description
Technical Field
The invention relates to the technical field of optical measurement, in particular to an intensity background light suppression method for computational imaging.
Background
Non-interference phase recovery is a widely used computational imaging technique, which greatly simplifies the hardware requirements of the conventional optical imaging system and reduces the influence of inherent aberration. Iterative phase recovery, one of the methods of non-interferometric PR, allows reconstruction of the required field from a series of acquired images.
For example, chinese patent publication No. CN105403508A discloses a non-interference phase imaging method based on a synthetic phase transfer function, which includes first shooting a set of light intensity images at different depths where objects are exponentially distributed along an optical axis direction at intervals with a camera, then solving an initial phase map according to the synthetic phase transfer function assuming that the objects are weakly absorbing and weakly phased, and finally substituting the initial phase map into an iterative compensation algorithm of the synthetic phase transfer function to solve an accurate phase map.
Chinese patent publication No. CN112629678A discloses a fast phase recovery method for general shape non-diffraction iterative computation, which decomposes the wavefront to be measured using a numerical orthogonal polynomial pattern, then computes a diffraction basis function for each numerical orthogonal polynomial based on fast fourier transform, and then iteratively solves a coefficient gradient between diffraction surfaces by using matrix operation, thereby realizing the wavefront detection of a high-speed general shape.
The high flexibility and high versatility make iterative PR an easy-to-access and easy-to-deploy tool, particularly suitable for research and diagnosis of wavefront sensing, super-resolution microscopy, and quantitative phase imaging. Iterative PR uses forward and backward fourier transforms to establish the relationship between the inverted field and the measured intensity field, typically involving estimating complex distributions from the corresponding intensity distributions under the constraints of experimental model parameters. Iterative PR is an inverse problem in optics and may be non-unique. The multi-image PR preferably eliminates local minimum lag.
The performance of PR methods depends fundamentally on the quality of the recorded intensity data and the accuracy of the match between the numerical PR model and the actual experimental system. Relaxed support constraints can also affect reconstruction accuracy. Acquired intensity images with low background and noise levels are a necessary condition for a high precision iterative PR method. In the PR model, the dominant noise sources are camera noise, including dark shot noise, read noise, and photon shot noise. Dark shot noise subject to poisson statistics is independent of signal level, but dependent on the temperature of the sensor; the reading noise is a fixed noise of the camera; photon shot noise follows a poisson distribution as intensity varies. Furthermore, the influence of the background is not negligible. Ambient light in an optical plant can cause background non-uniformity in the recorded image.
Currently, researchers pay more attention to noise removal and neglect background light suppression, and the quality of the background light suppression directly affects the accuracy of phase recovery wavefront detection.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an intensity background light suppression method for computational imaging, which obtains a support domain outside a light spot through mathematical modeling, realizes background light suppression and removal based on a polynomial, simplifies the acquisition process of a computational imaging image, expands the application range of computational imaging and improves the precision of wavefront reconstruction.
A method for restraining background light with intensity for calculating imaging is applied to a scene of collecting a light intensity diagram, wherein a beam expander, a flat plate to be tested, a convergent lens and an image sensor are sequentially arranged on an emergent light path of a laser, and the method comprises the following steps:
s1: moving the image sensor, and acquiring n defocused diffraction spots containing the wavefront error of the flat plate to be detected at different defocused distances;
s2: respectively setting the focal length s of the convergent lens, the caliber D and the out-of-focus position z of each out-of-focus diffraction spot j Setting the initial complex amplitude of the measuring surface as a full matrix;
s3: setting a pixel size d of an image sensor n And the number of pixels M 0 ×N 0 For each defocusing diffraction spot, obtaining effective defocusing diffraction spots
Central position (x) of j ,y j ) And off-focus diffraction spots with dimension of M multiplied by M;
s4: based on scalar diffraction theory, calculating the initial complex amplitude diffraction of the measuring surface to each out-of-focus surface according to the parameters of the imaging system to obtain the estimated light spot of each out-of-focus surface
For estimating light spots
Binarization is carried out to obtain a binary mask M j ；
S5: for each effectively defocused diffraction spot
The background light is roughly removed, namely the average value of redundant light intensity is calculated by the formula
Wherein A is j Is the average of the redundant light intensities;
s6 effective defocusing diffraction spot processed by the S5
Reconstructing the wavefront to be measured by using a phase recovery algorithm;
s7, calculating the corresponding defocused diffraction light spots based on the wave front to be measured reconstructed in S6, and calculating to obtain the corresponding mask plate M 'by using the method in S4' j Using the mask plate M' j Calculating to obtain N by polynomial processing z Polynomial of item number
S8: calculating the obtained mask M 'by using S7' j Extracting redundant light intensity, wherein the formula is as follows:
fitting the redundant light intensity by using the numerical polynomial S7 to obtain a fitting coefficient, wherein the formula is as follows:
s9: calculating the background light intensity S j First, before calculation using S8
Term coefficient combined with zernike polynomial Z i (u, v) superimposing, and superimposing the rest coefficients with a numerical polynomial;
s10: removing background light intensity S j The formula is as follows:
s11: and reconstructing the wavefront to be measured by using a phase recovery algorithm.
Further, in step S3, the effective defocus diffraction spot is calculated based on the centroid method
Central position (x) of j ,y j ) And an out-of-focus diffraction spot of dimension mxm.
In step S4, the spot is estimated
The formula for binarization is:
wherein σ 1 Is an empirical value and j is the index of the jth out-of-focus diffracted spot.
In step S5, the average value of the redundant light intensity is calculated by the following formula:
in the formula, n and m represent the order of the polynomial.
In steps S6 and S11, the phase recovery algorithm is the GS algorithm.
In step S7, the mask plate M 'is used' j To polynomial positionPhysical calculation to obtain N z Polynomial of term value
The formula of (1) is:
wherein Z is i (u, v) is a Zernike polynomial applied to calculate a numerical polynomial, and i is an index of the polynomial.
In step S8, the method of calculating the coefficient is a least square method.
In step S9, the background light intensity S is calculated j The formula of (1) is:
in the formula, c i And fitting the redundant light intensity for the numerical polynomial to obtain a coefficient.
Compared with the prior art, the invention has the following beneficial effects:
according to the invention, background light of diffraction spots is removed through polynomial fitting, and firstly, a non-uniform background can be corrected by using a numerical polynomial; the other is to predict the background of the light intensity effective part by using some polynomials according to the fact that the wavefront of the natural light is smooth. During image reconstruction, a background correction method may be iteratively performed to enhance the effect of removing the background.
Drawings
FIG. 1 is a schematic diagram of an apparatus for calculating an intensity background light suppression method for imaging according to an embodiment of the present invention;
FIG. 2 is a flow chart of an intensity backlight suppression method for computed imaging according to the present invention;
FIG. 3 is a diagram illustrating the recovery results of the method and the mean value elimination method according to the present invention.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
As shown in fig. 1, as an example of collecting a light intensity pattern, a beam expander 2, a flat plate 3 to be measured, a converging lens 4, and an image sensor 5 are sequentially arranged on an outgoing light path of a laser 1, and the image sensor 5 is fixed on a precision guide rail 6.
As shown in fig. 2, an intensity background light suppression method for computed imaging includes the following steps:
s1: and moving the image sensor, and acquiring n defocused diffraction spots containing the wavefront error of the flat plate to be detected at different defocused distances.
S2: respectively setting the focal length s, the caliber D and the defocusing position z of each defocusing diffraction spot of the convergent lens k The initial complex amplitude of the measurement plane is set to be a full matrix.
S3: setting image sensor pixel size d n And the number of pixels M 0 ×N 0 For each defocusing diffraction spot, obtaining effective defocusing diffraction spots
Central position (x) of j ,y j ) And an out-of-focus diffraction spot of dimension mxm.
S4: based on scalar diffraction theory, calculating the initial complex amplitude diffraction of the measuring surface to each out-of-focus surface according to the parameters of the imaging system to obtain the estimated light spot of each out-of-focus surface
Binarizing the estimated light spot to obtain a binary mask
Wherein σ 1 Is an empirical value, j is the index of the jth out-of-focus diffraction spot;
s5: for each effective separationFocal diffraction spot
Rough removal of background light, i.e. average of redundant light intensity
Wherein the average value of the redundant light intensities is calculated by the following formula:
s6, reconstructing the wavefront to be detected by using the defocused diffraction spots processed by the S5 and a phase recovery algorithm;
s7, calculating corresponding defocused diffraction light spots based on the wave front to be measured reconstructed in S6, and calculating corresponding mask plate M 'by using the method in S4' j Using the mask plate M' j Calculating the polynomial to obtain N z Polynomial of term value
Wherein, Zernike polynomial Z i (u, v) is applied to the arithmetic numerical polynomial and i is the index of the polynomial.
S8: mask M 'prepared from S7' j The redundant light intensity is extracted and,
fitting the redundant light intensity by using the numerical polynomial in the S6 to obtain a coefficient;
s9: background light intensity calculation first uses S8 before calculation
The term coefficients are combined with polynomial superposition, and the rest coefficients are superposed with numerical polynomial
S10: the background light is removed
S11: and reconstructing the wavefront to be measured by using a phase recovery algorithm.
The center position calculation method and the effective spot area determination described in consideration of the calculation speed and the calculation accuracy S3 are calculated based on the centroid method.
The phase recovery algorithm described in S6 and S11 is the GS algorithm, taking into account the speed and accuracy requirements of the wavefront reconstruction.
In order to consider the correspondence between the polynomial and the aberration and the orthogonality of the polynomial, the polynomials in S7 and S9 are zernike polynomials.
The method of calculating coefficients described in S8 is a least square method in consideration of the polynomial fitting accuracy.
A specific example of the method of the present invention is given below to illustrate the technical effect of the method of the present invention.
Here, s is 1079 for focal length selection . 41mm，z 1 ,z 2 ,z 3 ＝[-10,-15,-20]mm, bore D22 . 9mm, total number of iterations N of wavefront measurement 5000, number N of Zernike polynomials z ＝50，
The effective spot number is 1024 × 1024.
Three defocusing diffraction images are collected to carry out wave front phase and amplitude reconstruction, non-uniform background light is added in the three defocusing diffraction spots, the selected diffraction calculation model is a Fresnel diffraction model, and FIG. 3 is a recovery result graph of the method and the average value elimination method. Wherein (a) and (d) are the recovered phase and amplitude of the method of the present invention, (b) and (e) are the recovered phase and amplitude of the mean value elimination method, and (c) and (f) are the phase and amplitude of the real map. It can be seen from the figure that the method proposed herein is more efficient than the conventional method.
The embodiments described above are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only specific embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the present invention.
Claims (8)
1. The utility model provides an intensity background light suppression method for calculation formation of image, is applied to the scene that the light intensity map was gathered, has arranged beam expander, the flat board that awaits measuring, convergent lens, image sensor in proper order on the emergent light path of laser instrument, its characterized in that includes following steps:
s1: moving the image sensor, and acquiring n defocused diffraction spots containing the wavefront error of the flat plate to be detected at different defocused distances;
s2: respectively setting the focal length s, the caliber D and the defocusing position z of each defocusing diffraction spot of the convergent lens j Setting the initial complex amplitude of the measuring surface as a full matrix;
s3: setting a pixel size d of an image sensor n And the number of pixels M 0 ×N 0 For each defocusing diffraction spot, obtaining effective defocusing diffraction spots
Central position (x) of j ,y j ) And defocusing diffraction spots with dimension of M multiplied by M;
s4: based on scalar diffraction theory, according to the parameters of the imaging system, the initial complex amplitude diffraction of the measuring surface is calculated to each defocusing surface to obtain the estimated light spot of each defocusing surface
For estimating light spot
Binarization is carried out to obtain a binary mask M j ；
S5: for each effectively defocused diffraction spot
The background light is roughly removed, namely the average value of redundant light intensity is calculated by the formula
Wherein, A j Is the average of the redundant light intensities;
s6 effective defocusing diffraction spot processed by the S5
Reconstructing the wavefront to be detected by using a phase recovery algorithm;
s7, calculating corresponding defocused diffraction light spots based on the wave front to be detected reconstructed in S6, and calculating to obtain corresponding mask plate M 'by using the method in S4' j Using the mask plate M' j Processing the polynomial to obtain N z Polynomial of term value
S8: mask M 'obtained by calculation through S7' j Extracting redundant light intensity, wherein the formula is as follows:
fitting the redundant light intensity by using the numerical polynomial S7 to obtain a coefficient, wherein the formula is as follows:
s9: calculating the background light intensity S j First, before calculation using S8
The coefficient of the neck in combination with Zernike polynomials Z i (u, v) superimposing, and superimposing the rest coefficients with a numerical polynomial;
s10: removing background light intensity S j The formula is as follows:
s11: and reconstructing the wavefront to be detected by using a phase recovery algorithm.
2. The intensity backlight suppression method for computed imaging according to claim 1, wherein in step S3, effective out-of-focus diffraction spots are calculated based on centroid method
Central position (x) of j ,y j ) And an out-of-focus diffraction spot of dimension mxm.
3. The method for suppressing intensity background light for computed imaging according to claim 1, wherein in step S4, the estimated light spot is processed
The formula for binarization is:
wherein σ 1 Is an empirical value and j is the index of the jth out-of-focus diffracted spot.
4. The method of claim 1, wherein in step S5, the average value of the redundant light intensity is calculated by the following formula:
in the formula, n and m represent the order of the polynomial.
5. The method of claim 1, wherein the phase-recovery algorithm is GS algorithm in steps S6 and S11.
6. The intensity background light suppression method for computed tomography according to claim 1, wherein in step S7, the mask plate M 'is used' j Processing the polynomial to obtain N z Polynomial of item number
The formula of (1) is:
wherein Z is i (u, v) is a Zernike polynomial applied to calculate a numerical polynomial, and i is an index of the polynomial.
7. The method for suppressing background light with intensity used for computed imaging according to claim 6, wherein in step S8, the method for computing the coefficient is least squares method.
8. Intensity backlight suppression method for computed imaging according to claim 6The method is characterized in that in step S9, the background light intensity S is calculated j The formula of (1) is:
in the formula, c i And fitting the redundant light intensity for the numerical polynomial to obtain a coefficient.
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| US20170168285A1 (en) * | 2015-12-14 | 2017-06-15 | The Regents Of The University Of California | Systems and methods for image reconstruction |
| CN113188671A (en) * | 2021-04-27 | 2021-07-30 | 浙江大学 | Wavefront detection method based on cross iteration automatic position correction |
| US20220003633A1 (en) * | 2019-07-18 | 2022-01-06 | Zhejiang University | Device and method for detecting wavefront error by modal-based optimization phase retrieval using extended nijboer-zernike theory |
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| US20170168285A1 (en) * | 2015-12-14 | 2017-06-15 | The Regents Of The University Of California | Systems and methods for image reconstruction |
| US20220003633A1 (en) * | 2019-07-18 | 2022-01-06 | Zhejiang University | Device and method for detecting wavefront error by modal-based optimization phase retrieval using extended nijboer-zernike theory |
| CN113188671A (en) * | 2021-04-27 | 2021-07-30 | 浙江大学 | Wavefront detection method based on cross iteration automatic position correction |
Non-Patent Citations (2)
| Title |
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| "Hybrid phase retrieval from a single defocused image", 《SPIE》, 5 August 2015 (2015-08-05) * |
| 李斐;饶长辉;: "基于离焦光栅的最小二乘波前复原算法", 中国激光, no. 11, 10 November 2010 (2010-11-10) * |
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