CN109708842B - Camera lens point spread function measuring method based on single-pixel imaging - Google Patents
Camera lens point spread function measuring method based on single-pixel imaging Download PDFInfo
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Abstract
The invention relates to a single-pixel imaging-based camera lens Point Spread Function (PSF) (Point Spread function) measurement method, which can effectively improve the signal-to-noise ratio of PSF measurement while realizing point Spread function PSF measurement of full-field spatial variation. Before measurement, a Liquid Crystal Display (LCD) is placed vertically along the optical axis of the camera. During measurement, firstly, a basic image mode required by single-pixel imaging is displayed on a liquid crystal display screen, and a camera is adopted for shooting to obtain an image; secondly, calculating the light transmission coefficient from each point on the liquid crystal display screen to a single pixel on the camera image according to the single pixel imaging principle; performing single-pixel imaging on all pixels on the camera image to obtain light transmission coefficients from all points on the liquid crystal display screen to all pixels on the camera image; and finally, calculating to obtain a point spread function from any point on the liquid crystal display screen to the camera image according to the light transmission coefficients of all the pixel points on the camera image. The method can obtain the measurement result of the camera lens point spread function PSF with higher signal-to-noise ratio than that of the traditional star point method under the same camera exposure time.
Description
Technical Field
The invention relates to a camera lens point spread function measuring method based on single-pixel imaging, which improves the signal-to-noise ratio of point spread function PSF measurement and realizes PSF measurement of spatial variation. The invention belongs to the field of computational imaging.
Background
The point spread function PSF mainly characterizes the brightness distribution formed by the point light source after passing through the optical system, and is an important parameter for describing the image blur caused by the optical system aberration, defocus, and other factors during the imaging process. The method can better reflect the performance of the camera lens and is also the basis for image restoration.
Most of the existing PSF measurement methods consider PSF models as symmetrical and space-invariant models, so that the existing PSF measurement methods have certain limitation and are only suitable for partial imaging systems. Although the PSF can be obtained theoretically by changing the spatial position of the point light source, the PSF cannot be measured accurately by using a common point light source because of low signal-to-noise ratio, and the PSF cannot be measured spatially by using a method of generating a point light source by using laser because the imaging position of the point light source is difficult to change. Therefore, how to solve the problem that the high snr cannot be compatible with the spatial variation measurement becomes a key of the spatial variation PSF measurement.
In the single-pixel imaging technology developed in recent years, due to the characteristics of high imaging signal-to-noise ratio and high resolution imaging, a new idea is provided for solving the problem of PSF measurement of spatial variation. If a single-pixel imaging technology can be applied to each pixel of the camera and the PSF is measured by using the technology, a spatial image blur kernel aiming at each pixel, namely the PSF with spatial variation, can be obtained, and meanwhile, the signal-to-noise ratio in the measurement process can be effectively improved, so that the PSF with high signal-to-noise ratio and spatial variation can be measured.
Disclosure of Invention
The invention provides a camera lens point spread function PSF measuring method based on single-pixel imaging, which can improve the signal-to-noise ratio during measurement of a spatial variation point spread function. The basic principle of the method is that a point spread function with space change is regarded as an optical transmission coefficient between an object space point and an image plane point, the optical transmission coefficients of the whole camera image plane point and an object plane (liquid crystal display screen) point are obtained by using a single-pixel imaging technology, and the point spread function from the point on the liquid crystal display screen to the point on the camera image is formed through conversion and recombination.
Camera imaging system, image can be modeled as a point spread function PSF of a lens
Where O denotes a sharp image, I denotes a blurred image after degradation, (x, y) denotes an object plane coordinate system, (u, v) denotes an image plane coordinate system, Ω denotes an area where an input sharp image is observed, and h (u, v; x, y) denotes a light transmission coefficient from a point (x, y) on the object plane (liquid crystal display screen) to a camera image plane point (u, v).
If we can treat each pixel (u, v) of the camera as a single pixel detector, by modulating the input scene O (x, y) as some transformed basis function or basis image, then equation (1) can also be understood as the coefficient H (u, v; m, n) in the transformed domain of the light transmission coefficient H (u, v; x, y) acquired by the single pixel detector (u, v) in some measurement, which can be expressed as:
h (u, v; m, n) is a coefficient in the transform domain of the light transmission coefficient (image) corresponding to the camera pixel (u, v), r (u, v; x, y, m, n) represents the positive transform basis function or basis image generated by the modulated input scene, and Ω' represents the corresponding region where the input scene is modulated. After all the coefficients in the transform domain have been acquired, they are inverse transformed by:
s (u, v; x, y, m, n) denotes the corresponding inverse transform basis function or basis image and phi denotes the corresponding region in the transform domain. Equations (2) and (3) indicate that the light transmission coefficient h (x, y; u, v) for any pixel of the image in the full field of view of the camera can be obtained by single pixel imaging techniques. And finally, converting and recombining according to the light transmission coefficients of all pixel points on the camera image to obtain a point spread function from a point on the liquid crystal display screen to the point on the camera image.
In the present invention, any single-pixel imaging technique can be used for measuring the point spread function, and in consideration of the fact that in recent years, the single-pixel imaging method based on the orthogonal basis has a higher signal-to-noise ratio and can reconstruct a high-quality image, in practice, the single-pixel imaging method based on the fourier transform is specifically adopted for measuring the point spread function.
The technical solution of the invention is as follows: firstly, a liquid crystal display screen is used for displaying a series of base image modes required by single-pixel imaging, a camera is used for shooting and obtaining images, single-pixel imaging is carried out on each camera pixel, and finally, the imaging result is converted to obtain a camera lens point spread function PSF. The measuring process mainly comprises the following steps:
(1) firstly, vertically placing a liquid crystal display screen along an optical axis of a camera;
(2) displaying a basic image mode required by single-pixel imaging on a liquid crystal display screen, and shooting by adopting a camera to obtain an image;
(3) calculating an image corresponding to a single pixel on the camera image according to a single-pixel imaging principle so as to obtain a light transmission coefficient from each point on the liquid crystal display screen to the single pixel on the camera image;
(4) performing single-pixel imaging on all pixels on the camera image to obtain light transmission coefficients from all points on the liquid crystal display screen to all pixel points on the camera image;
(5) and according to the light transmission coefficients of all pixel points on the camera image, taking out the values of the same point of the liquid crystal display screen from the light transmission coefficients, and recombining the values to form a point spread function from the point on the liquid crystal display screen to the camera image.
The liquid crystal display screen in the step (1) should be able to be completely located in the camera view field, the resolution of the liquid crystal display screen should be higher than that of the camera view field, and the screen display area should correspond to the area of the PSF to be tested of the camera.
The base image mode in the step (2) is a sinusoidal stripe image mode with different frequencies of two-dimensional Fourier transform, and each frequency comprises a four-step phase shift image mode. And shooting and acquiring a corresponding image through a camera.
The single-pixel imaging technology in the step (3) is to calculate and obtain a two-dimensional Fourier transform domain coefficient of a lens Point Spread Function (PSF) of the camera according to four-step phase-shift fringe images with different frequencies shot by the camera; and after all coefficients of the two-dimensional Fourier transform domain image are acquired, performing inverse Fourier transform on the transform domain image, and calculating to obtain the light transmission coefficient from any point on the liquid crystal display screen to the camera pixel.
The point spread function from the point on the liquid crystal display screen formed by recombination in the step (5) to the camera image is as follows:
for each pixel (u) of the camera i ,v i ) Light transmission coefficient h (u) obtained by single-pixel imaging i ,v i (ii) a x, y) (i ═ 1,2, …, w × h; w and h are resolution of u-axis and v-axis of the camera image, respectively), and a coordinate point (x) identical to that on the liquid crystal display screen is extracted therefrom 0 ,y 0 ) Corresponding light transmission coefficient value h (u) i ,v i ；x 0 ,y 0 ). By correlating each image with a coordinate point (x) on the screen 0 ,y 0 ) Related h (u) i ,v i ；x 0 ,y 0 ) All are combined to obtain the point (x) on the screen 0 ,y 0 ) As a light spot, the intensity distribution it forms on the camera pixel plane, i.e. the camera lens point spread function h' (x) obtained by the conventional method 0 ,y 0 (ii) a u, v). Dot (x) on liquid crystal display screen 0 ,y 0 ) Camera lens point spread function h' (x) 0 ,y 0 (ii) a u, v) at any point (u) i ,v i ) The specific calculation formula of the numerical value is as follows:
h′(x 0 ,y 0 ；u i ,v i )＝h(u i ,v i ；x 0 ,y 0 ). (4)
the invention has the advantages that:
(1) the signal to noise ratio is measured. By applying single-pixel imaging to PSF measurement, the signal-to-noise ratio of PSF measurement is effectively improved, and compared with the traditional star point method, the measurement result with higher signal-to-noise ratio can be obtained in the same exposure time.
(2) A measurement of the spatially varying point spread function PSF can be achieved. According to the invention, each pixel of the camera is subjected to single-pixel imaging, so that an image blur kernel (namely a point spread function) of each pixel of the camera is obtained, and a blur model of a camera lens can be better attached.
(3) Compared with a star point method based on a laser light source, the invention has the advantages of simple measuring system structure, lower measuring equipment cost and simple and convenient measuring process.
In a word, the point spread function PSF measuring method based on single-pixel imaging effectively improves the measuring signal-to-noise ratio of the point spread function PSF, and can realize the point spread function PSF measurement of the camera lens space change. Meanwhile, the cost of hardware equipment required by the invention is lower, and the measurement is convenient to implement.
Drawings
FIG. 1 is a flow chart of a point spread function PSF measurement in accordance with an embodiment of the present invention.
FIG. 2 is a system block diagram of the present invention in operation. In the figure, 1 is a liquid crystal display screen for displaying a sine stripe pattern, 2 is a camera, and 3 is a computer.
FIG. 3 is a schematic diagram of the principle of the present invention for light transmission coefficient (image) measurement using Fourier single pixel imaging. In the figure, 4 is a liquid crystal display, 5 is a partial sinusoidal fringe pattern used in fourier single-pixel imaging, 6 is a camera lens and a camera to be measured, 7 is a schematic plane view of a camera pixel, 8 is a two-dimensional fourier transform domain coefficient of an optical transmission coefficient (image) obtained by performing four-step phase shift calculation on a single pixel of the camera, and 9 is an optical transmission coefficient (image) of a camera image pixel obtained by performing inverse fourier transform on the two-dimensional fourier transform domain coefficient.
Fig. 4 is a schematic diagram of a result of a point spread function PSF of a conventional camera obtained by converting an optical transmission coefficient (image) obtained by the fourier single-pixel technique according to the present invention. In the figure, 10 is an image pattern displayed on a liquid crystal display, 11 is a camera lens to be measured, 12 is a camera pixel plane, 13 is a result of an optical transmission coefficient (image) obtained by a fourier single-pixel imaging technique, 14 is a result of a point spread function PSF of a conventional camera lens after transformation, and 15 is a computer for calculating and generating stripes.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings and the detailed description.
The invention is based on the single-pixel imaging principle, and the main measurement system of the invention is shown in figure 2 and mainly comprises a liquid crystal display screen, a camera and a computer. The point spread function of the spatial variation is regarded as the light transmission coefficient between an object space point and an image plane point, the light transmission coefficients of the whole image plane point and the object plane (liquid crystal display screen) point are obtained by performing single-pixel imaging on all pixels, and then the point spread function PSF of the camera lens is obtained by extracting the light transmission coefficients related to the same object point from the light transmission coefficients. In specific implementation, the single-pixel imaging adopts a Fourier single-pixel imaging principle, a liquid crystal display screen is used for displaying a series of sine stripe modes required by the Fourier single-pixel imaging, a camera is used for shooting stripe images and carrying out Fourier single-pixel imaging on each camera pixel, and finally, the light transmission coefficient measurement result is converted to obtain a camera lens point spread function PSF. The specific operation is as follows:
1. the lcd panel is first placed vertically along the optical axis of the camera. The liquid crystal display screen can be completely positioned in the camera view field, the resolution of the liquid crystal display screen is higher than that of the camera view field, and the screen display area corresponds to the PSF area to be tested of the camera.
2. And displaying a basic image mode required by single-pixel imaging on the liquid crystal display screen, and shooting by adopting a camera to obtain an image.
When the Fourier single-pixel imaging principle is adopted, the base image mode is a two-dimensional Fourier transform sine stripe image mode with different frequencies, and each frequency comprises a four-step phase shift image mode. The computer firstly generates a sine stripe pattern required by Fourier single-pixel imaging
And displayed on the liquid crystal display panel, as shown in fig. 3(4) and (5), in the following manner:
wherein (x, y) represents a point on the plane coordinate system of the liquid crystal display screen, (f) x ,f y ) Representing the spatial frequency of the sinusoidal fringes,
representing the phase of the sinusoidal image, a is the average brightness of the image, and b is the amplitude of the sinusoidal pattern.
The values of (0, pi/2, pi, 3/2 pi) respectively form a four-step phase shift image mode.
Capturing images using a camera screen
As shown in fig. 3, the expression for the camera pixel response is:
where Ω denotes the area of the screen where the stripes are displayed, (u, v) denotes the coordinates of the camera pixel plane, h (u, v; x, y) denotes the spatially varying point spread function of the camera lens corresponding to the camera pixel (u, v), R n Indicating the response of the camera to ambient light.
3. And then, according to a single-pixel imaging technology, calculating an image corresponding to a single pixel on the camera image so as to obtain the light transmission coefficient from each point on the liquid crystal display screen to the single pixel on the camera image.
Let a single pixel coordinate on the camera image be (u) 0 ,v 0 ) For Fourier single pixel imaging, each spatial frequency (f) x ,f y ) By using a four-step phase shift method, phases are respectively displayed as
The fringe of (0, pi/2, pi, 3/2 pi) is calculated accordingly, and the coefficient of the pixel light transmission coefficient (image) corresponding to the frequency in the two-dimensional fourier transform domain is obtained, as shown in fig. 3(8), which can be expressed as:
wherein exp [ -j2 π (f) x x+f y y)]A two-dimensional fourier transform kernel is shown. H (u) 0 ,v 0 ；f x ,f y ) Is the light transmission coefficient (image) h (u) 0 ,v 0 (ii) a x, y) of the two-dimensional fourier transform domain coefficients. In order to acquire an image of an M × N resolution size, it is necessary to acquire coefficients of M × N fourier transform domains. M is the number of effective display pixels of the liquid crystal display screen along the x direction, and N is the number of effective display pixels of the liquid crystal display screen along the y direction. After all coefficients in the Fourier transform domain image are obtained, performing inverse Fourier transform on the Fourier transform domain image, and comprising the following steps:
h(u 0 ,v 0 ；x,y)＝IFT(H(u 0 ,v 0 ；f x ,f y )). (8)
wherein IFT represents the inverse fourier transform. The result is h (u) 0 ,v 0 (ii) a x, y) is an image, as shown in fig. 3(9), which shows that any point (x, y) to a pixel point (u) of the camera in the effective display area with resolution of M × N on the screen 0 ,v 0 ) The optical transmission coefficient of (1).
4. Performing the single-pixel imaging of the step 3 on all the pixels on the camera image to obtain the light transmission coefficients h (u) from all the points on the liquid crystal display to all the pixel points on the full view field of the camera image i ,v i (ii) a x, y) (i ═ 1,2, …, w × h; w and h are resolution of the u-axis and v-axis, respectively, of the camera image).
5. According to the light transmission coefficient h (u) of all pixel points on the camera image i ,v i (ii) a x, y) taking out the same point (x) of these light transmission coefficients for the liquid crystal display panel 0 ,y 0 ) The values of (a) are recombined to form a point spread function from the point on the liquid crystal display to the point on the camera image.
In step 4, the light transmission coefficient (image) from the camera pixel perspective is obtained, whereas the conventional camera lens point spread function PSF is the camera lens point spread function PSF from the object light point perspective, and therefore, the light transmission coefficient measurement results need to be converted to obtain the camera lens point spread function.
The conversion method is shown in fig. 4, and the main principle is as follows: light transmission coefficient h (u) obtained for single-pixel imaging of each pixel of a camera i ,v i (ii) a x, y) as shown in FIG. 4(13), and extracting the same coordinate point (x) as that on the liquid crystal display screen 0 ,y 0 ) Corresponding value h (u) i ,v i ；x 0 ,y 0 ). By correlating each image with a coordinate point (x) on the screen 0 ,y 0 ) H (u) of interest i ,v i ；x 0 ,y 0 ) All are combined to obtain the point (x) on the screen 0 ,y 0 ) As a light spot, the brightness distribution formed on the pixel plane of the camera is shown in fig. 4(14), i.e. the point spread function h' (x) of the camera lens obtained by the conventional method 0 ,y 0 ；u,v)。
Dot (x) on liquid crystal display screen 0 ,y 0 ) Camera lens point spread function h' (x) 0 ,y 0 (ii) a u, v) at any point (u) i ,v j ) The specific calculation formula of the numerical value is as follows:
h′(x 0 ,y 0 ；u i ,v j )＝h(u i ,v j ；x 0 ,y 0 ). (9)。
Claims (3)
1. a method for measuring a Point Spread Function (PSF) of a camera lens based on single-pixel imaging is characterized by comprising the following steps:
(1) firstly, vertically placing a liquid crystal display screen along an optical axis of a camera;
(2) displaying a basic image mode required by single-pixel imaging on a liquid crystal display screen, and shooting by adopting a camera to obtain an image; the base image mode is a two-dimensional Fourier transform sine stripe image mode with different frequencies, each frequency comprises a four-step phase shift image mode, and a camera shoots and collects corresponding images;
(3) then, according to a single-pixel imaging technology, calculating an image corresponding to a single pixel on the camera image, thereby obtaining the light transmission coefficient from each point on the liquid crystal display screen to the single pixel on the camera image; the single-pixel imaging technology is characterized in that four-step phase-shift fringe images with different frequencies are shot by a camera, two-dimensional Fourier transform domain coefficients of a camera lens point spread function PSF are obtained through calculation, after all coefficients of the two-dimensional Fourier transform domain images are obtained, inverse Fourier transform is conducted on the transform domain images, and light transmission coefficients from any point on a liquid crystal display screen to a camera pixel are obtained through calculation;
(4) performing single-pixel imaging on all pixels on the camera image to obtain light transmission coefficients from all points on the liquid crystal display screen to all pixel points on the camera image;
(5) and according to the light transmission coefficients of all pixel points on the camera image, taking out values corresponding to the same point of the liquid crystal display screen from the light transmission coefficients, and recombining the values to form a point spread function from the point on the liquid crystal display screen to the camera image.
2. The method of claim 1, wherein: the liquid crystal display screen in the step (1) should be able to be completely located in the camera view field, the resolution of the liquid crystal display screen should be higher than that of the camera view field, and the screen display area should correspond to the PSF area to be tested of the camera.
3. The method of claim 1, wherein: the point spread function from the point on the liquid crystal display screen to the camera image formed by recombination in the step (5) is as follows:
for each pixel (u) of the camera i ，v i ) Light transmission coefficient h (u) obtained by single-pixel imaging i ，v i (ii) a x, y), wherein,
i＝1，2，...，w×h，
here, w and h are resolution of the u-axis and v-axis of the camera image, respectively, (x, y) represent coordinates of points on the object plane liquid crystal display screen, in which the same coordinate points (x) as those on the liquid crystal display screen are extracted 0 ，y 0 ) Corresponding light transmission coefficient value h (u) i ，v i ；x 0 ，y 0 ) (ii) a By correlating each image with a coordinate point (x) on the screen 0 ，y 0 ) Related h (u) i ，v i ；x 0 ，y 0 ) All are combined to obtain the point (x) on the screen 0 ，y 0 ) As a light spot, its brightness distribution formed at the camera pixel plane, i.e. a camera obtained by conventional methodsLens point spread function h' (x) 0 ，y 0 (ii) a u, v), where (u, v) denotes image plane coordinate system coordinates; dot (x) on liquid crystal display screen 0 ，y 0 ) Camera lens point spread function h' (x) 0 ，y 0 (ii) a u, v) at any point (u) i ，v i ) The specific calculation formula of the numerical value is as follows:
h′(x 0 ，y 0 ；u i ，v i )＝h(u i ，v i ；x 0 ，y 0 )。
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| CN112991299A (en) * | 2021-03-18 | 2021-06-18 | 中国科学院紫金山天文台 | Method for constructing smooth point diffusion function in image processing |
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