Method and device for measuring lateral magnification of optical system

A technology of lateral magnification and optical system, applied in the field of metrology equipment, can solve the problem of low repeatability of lateral magnification measurement, achieve the effect of improving the repeatability of measurement results, reducing errors, and improving repeatability

Active Publication Date: 2012-07-25

HARBIN INST OF TECH

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[0028] The present invention aims at the large distortion optical system of the above-mentioned existing measurement method, which is not suitable for measurement in a large field of view, but in a small field of view, there is the problem of low repeatability of lateral magnification measurement, and the existing measurement device has the problem of separation In view of the problem of focusing, a metho...

Abstract

The invention discloses a method and a device for measuring lateral magnification of an optical system, belonging to the metering equipment field taking optical method as characteristic, wherein the method comprises the steps of taking line light source as target to obtain a linear image; finding value range of the pixel distance in the frequency domain; using the search algorithm to perform computing to obtain lateral magnification of the optical system according to that the overlap ratio of the actual modulation transfer function curve related to the pixel distance and the theoretical actual modulation transfer function curve is the best on the least squares condition; and the line light source is a bent shape in a plane determined by the optical axis direction of the device and row or line direction of the image sensor; any position of the line light source can image focally to the surface of the image sensor. The method for measuring lateral magnification of an optical system in the invention is beneficial for reducing error between single measurement results so as to improve repeatability of the measurement result.

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Testing optical properties

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Least squaresImage sensor +12

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[0052] The specific embodiments of the present invention will be described in further detail below in conjunction with the accompanying drawings.

[0053] figure 1 To use the line light source optical system lateral magnification measuring device structure schematic diagram, the plane optical path diagram is as follows figure 2 As shown; the device includes a line light source 1, an optical system 2, an image sensor 3. The line light source 1 is imaged onto the surface of the image sensor 3 through the optical system 2, and, in the optical axis direction of the device and the image sensor 3 line direction In the determined plane, the line light source 1 is curved, and any position on the line light source 1 is in-focus imaged onto the surface of the image sensor 3; wherein the horizontal length of the line light source 1 is 3mm, and the pixel pitch of the image sensor 3 is 5.6μm.

[0054] The method of measuring the lateral magnification of an optical system using a line light source, the flow chart is as follows image 3 As shown, the method steps are as follows:

[0055] a. Place a line light source 1 with a length of d=3mm on the object side, and the direction is parallel to the 3 rows of the image sensor;

[0056] b. The image sensor 3 images the line light source 1, such as Figure 4 As shown, the initial point spread function image is obtained; keeping the exposure time of the image sensor 3 unchanged, removing the line light source 1, the image sensor 3 images the background to obtain the interference image, and the maximum gray value in the interference image is used as the threshold, The threshold is 10;

[0057] c. From the initial point spread function image obtained in step b, extract the entire line of the line light source image as the initial line spread function image, such as Figure 5 As shown, and the gray value of the pixel whose gray value is less than the threshold value obtained in step b in the initial line extension function image is corrected to 0, the corrected line extension function image is obtained, such as Image 6 As shown, the modified line expansion function image has n=1280 elements;

[0058] or:

[0059] In the initial point spread function image obtained in step b, the gray value of the pixel whose gray value is less than the threshold value obtained in step b is corrected to 0, as the corrected point spread function image; and in the corrected point spread function image, the line light source Extract the entire line of information like the line to get the correction line expansion function image, such as Image 6 As shown, the modified line expansion function image has n=1280 elements;

[0060] d. Perform Discrete Fourier Transform and take the modulus on the correction line spread function image obtained in step c to obtain a modulation transfer function image, which has the same elements as the correction line spread function image obtained in step c The number n=1280, that is, 1280 discrete spectral components, which are respectively M in the descending order of spatial frequency 0 , M 1 , M 2 ,..., M 1279 , In this order, the modulation transfer function value corresponding to the first time the modulation transfer function value reaches the minimum value is M 42 , Its subscript serial number is i=42, combined with the pixel pitch l=5.6μm of the image sensor 3, we get M 41 And M 43 The corresponding spatial frequency value is: f min =(i-1)/(nl)=(42-1)/(1280×5.6×10 -3 )=5.7199lp/mm and f max =(i+1)/(nl)=(42+1)/(1280×5.6×10 -3 )=5.9989lp/mm;

[0061] e. According to the modulation transfer function model MTF(f)=|sinc(πfd′)|, combined with the spatial frequency range f obtained in step d min =5.7199lp/mm and f max =5.9989lp/mm, get the value range of the linear light source image length: d max ′=1/f min =nl/(i-1)=1280×5.6×10 -3 /(42-1)=0.1748mm and d min ′=1/f max =nl/(i+1)=1280×5.6×10 -3 /(42+1)=0.1667mm;

[0062] f. According to the length d of the line light source 1 in step a = 3mm and the length of the line light source image obtained in step e, the value range d min ′=0.1667mm and d max ′=0.1748mm, the calculated value range of the lateral magnification of the optical system is: β min =d min ′/D=nl/((i+1)d)=1280×5.6×10 -3 /((42+1)×3)=0.0556 and β max =d max ′/ d=nl/((i-1)d)=1280×5.6×10 -3 /((42-1)×3)=0.0583;

[0063] e. According to the modulation transfer function model MTF(f)=|sinc(πfd′)|, combined with the spatial frequency value f=5.8594lp/mm obtained in step d, the line source image length is obtained: d′=1/f= nl/i=1280×5.6×10 -3 /42=0.1707mm;

[0064] f. According to the length of the line light source 1 in step a = 3mm and the length of the line light source image obtained in step e d'= 0.1707mm, the lateral magnification ratio of the optical system 3 is calculated: β=d'/d=nl/(id )=1280×5.6×10 -3 /(42×3)=0.0569.

[0065] g. The value range β of the lateral magnification of the optical system 3 obtained in step f min =0.0556 and β max =0.0583, divide the horizontal magnification of the optical system 3 into N=1000, respectively, β 1 , Β 2 ,..., β 1000 , Where β 1 = Β min =0.0556, β 1000 = Β max =0.0583;

[0066] h. According to the order of the spatial frequency from small to large, draw the n=1280 modulation transfer function values obtained in step d into a curve, and select this curve from M 0 Start to the first maximum value, not including the M obtained in step d 42 , A total of K as the comparison data, the K modulation transfer function values are M K1 , M K2 ,..., M KK , Substituting the lateral magnification ratios of N=1000 optical systems obtained in step g into the following formulas: Among the N=1000 values obtained by this formula, the lateral magnification β of the optical system 3 corresponding to the minimum value is the obtained value, and after calculation, β=0.0558.

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