CN102607817A - Method and device for measuring lateral magnification of optical system - Google Patents

Abstract

The method and device for measuring the lateral magnification of an optical system using a line light source belong to the field of metering equipment characterized by the use of optical methods; the method uses a line light source as the target to obtain a linear image, and finds the value range of the pixel pitch in the frequency domain. And according to the actual modulation transfer function curve related to the pixel pitch and the theoretical modulation transfer function curve under the least squares condition, the coincidence degree is the best, and the lateral magnification of the optical system is calculated by using the search algorithm; In the plane determined by the row or column direction of the sensor, the line light source is curved, and any position on the line light source is quasi-focused and imaged on the surface of the image sensor; adopting the invention to measure the lateral magnification of the optical system is beneficial to reduce the single The error between the measurement results can be reduced, thereby improving the repeatability of the measurement results.

Description

Method and device for measuring lateral magnification of optical system using line light source

technical field

The method and device for measuring the lateral magnification of an optical system using a line light source belong to the field of metrology equipment characterized by the use of optical methods, and in particular relate to a method for measuring the lateral magnification of an optical system by using a line light source image in the frequency domain with a line light source as the target. Methods and devices.

Background technique

The lateral magnification of the optical system is a very important parameter in the field of medicine and precision measurement. It not only indicates the technical index of the optical system, but also can use this technical index to carry out precise measurement of other parameters. However, how to obtain the lateral magnification of an optical system is the primary problem in carrying out this work.

1. The measurement method of the lateral magnification of the optical system

In July 1987, "Medical Physics" published an article "On the Magnification of the Objective Lens in the Microscope", which found a contradiction between the empirical formula of the objective lens' lateral magnification in the microscope and the actual measurement process. However, this contradiction leads to the measurement of the lateral magnification of the optical system.

And some subsequent articles showed the necessity of measuring the lateral magnification of the optical system.

In March 1999, the article "Discussion on the Lateral Magnification in Geometric Optics" was published in Volume 1, Issue 2 of "Journal of Huangshan College", which discussed the mathematical expression of the lateral magnification of the optical system, and the application of this method The condition is ideal optical system imaging under paraxial conditions, but when these conditions are not satisfied, the error between the formula summarized in this paper and the lateral magnification of the actual optical system is not explained, and there is a lack of how to measure the optical system for this error. Description of the system lateral magnification method.

In May 2000, the second issue of "Journal of South China Normal University (Natural Science Edition)" published an article "Analysis and Application of the Transverse Magnification Curve of Ideal Optical System". It has a set of calculation formulas for lateral magnification, and draws the curve of lateral magnification-object distance and image distance. The applicable condition of this method is still the paraxial light of the ideal optical system, and for non-ideal conditions, the lateral magnification pointed out in the empirical formula The error between the magnification ratio and the actual lateral magnification ratio is not explained, which further illustrates the necessity of the method for measuring the lateral magnification ratio of the optical system.

In June 2002, "Journal of Jiangxi Institute of Education (Natural Science)" published the article "Using the phase transformation function to derive the object image distance formula and the lateral magnification formula of the lens under the paraxial condition" in the third issue of volume 23. Based on Liye optics, the object-image distance formula and the lateral magnification formula of the optical system under the paraxial condition are deduced by using the phase transformation effect of the lens. However, the applicable conditions of this article are still the ideal optics under the paraxial approximation condition System imaging also has the same problems as the previous two articles.

Because there is an urgent need to measure the lateral magnification of the optical system, some scholars have proposed their own measurement methods in the fields of medicine and precision measurement.

In September 2010, "Medical Imaging Technology" Volume 26 Supplement 1 published an article "Determination of the Intrinsic Magnification of Digital X-ray Machines", which provides a measurement method of magnification. This measurement method first fixes a small steel ball on the X On the line detector, use the ruler that comes with the machine to measure the diameter of the projection of the ball after taking the film; print out the photo, measure the diameter of the steel ball projected on the photo with a sub-gauge under the reading light, and use a vernier caliper to accurately measure its diameter. Data, compared the two sets of data error differences. Also use a vernier caliper to measure the actual diameter of the corresponding steel ball, and the ratio of the two diameters can be obtained, that is, the magnification ratio of the X-ray shadow line. Since this article was not written by a person in the field of precision measurement, the measurement method used in the article is relatively old, and the ruler is used to measure the height of the object. This kind of ruler measurement has a certain degree of subjectivity and has a great impact on the measurement results.

In September 2003, "Journal of Hebei Vocational and Technical Teachers College" Volume 17, Issue 3 published an article "Measurement of Telescope Magnification by Comparing Plate Method", which introduced a new method of lateral magnification of optical system, which is the same as Compared with the methods used in the current general physics experiments, not only the principle is simple, the data is accurate, but also more operable. However, this method still does not get rid of the shackles of the traditional method, and the judgment of the image height still uses the method of reading the target length with a scale, so it also has the problem of subjectivity.

However, this problem has been solved with the rapid development of CCD and its wide application in the field of precision measurement. At the same time, the measurement accuracy of the lateral magnification of the optical system has also been improved accordingly.

In June 1998, "Photoelectric Engineering" Volume 25, Issue 3 published an article "CCD Measuring Telescope System Magnification". The method introduced in this article is simple in principle, and directly uses the ratio of image height to object to measure the magnification of the telephoto system. , compared with the traditional method, the method introduced in this article does not use a ruler to measure the image height, but judges it by the product of the number of CCD pixels occupied by the reticle and the pixel pitch. This method reduces the measurement time. Subjective factors make the measurement results more accurate.

In March 2002, "Physical Experiments" Volume 22, Issue 3 published an article "Determination of the Base Point of a Compound Optical System by the Method of Lateral Magnification", in August 2006, an article "Lateral Magnification" was published in "University Physics" Volume 25, Issue 8 Ratio method to determine the base point of the optical system", these two articles extend the lateral magnification to a new application field, use it to determine the base point of the compound optical system, and draw an important conclusion, the base point is the lateral magnification of the optical system function. This conclusion shows that the accuracy of determining the base point is directly related to the accuracy of the lateral magnification of the optical system. Therefore, it is necessary to accurately measure the lateral magnification of the optical system. However, this paper still uses the definition of lateral magnification, that is, the ratio of image height to object height for measurement. Among them, the measurement principle of image height still follows the measurement principle of the previous article. According to the number of pixels spanned by the double slit and the pixel spacing multiplied to determine.

The following conclusions can be drawn from the description of the prior art methods. For the measurement of the lateral magnification of the optical system, there are no more than two methods:

1) Use the definition of the lateral magnification of the optical system, that is, the ratio of the image height to the object height to directly measure;

2) According to the specific relationship between the lateral magnification of the optical system and a certain image height in a specific optical system, the indirect measurement of the lateral magnification of the optical system is realized through the acquisition of the image height.

No matter which method is used, it is necessary to judge the image height, and the judgment method at this stage has the same technical characteristics:

The height information of the image is obtained by multiplying the number of pixels spanned by the image and the pixel pitch.

Although this technical feature can avoid the subjective factors in the process of measuring image height with a scale in the traditional method, this method also has its own problems, because the judgment of the number of pixels can only be an integer judgment, and the judgment of each side There is a maximum error of ±0.5 pixels, and there may be an error of ±1 pixel between the two edges. The smaller the size of the image, the greater the error will be. Although it is theoretically possible to increase the length of the line light source, it can be compensated by using more pixels to share the error, but for a large distortion optical system, that is, an optical system with different magnifications under different fields of view, increasing the length of the line light source is the same. will bring new problems:

1) Increasing the size of the target may cause serious deformation of the image in length. In this case, not only the error cannot be shared equally, but the error in judging the number of pixels will be larger. Therefore, for large distortion optical systems, this method is not suitable. Suitable for measurement in a large field of view;

2) For large-distortion optical systems, it is reasonable to accurately measure the lateral magnification in each small field of view, and finally obtain the lateral magnification curves in different fields of view. However, due to the measurement method used in the background technology In the small field of view, the error between single measurement results is large, so the measurement repeatability of the lateral magnification of the large distortion optical system is low.

2. Problems with the measuring device for lateral magnification of the optical system

International Patent Classification No. G01M 11/02 In the field of testing optical properties, two invention patents disclose the composition of the moving image modulation transfer function measurement device:

Patent No. ZL200810137150.1, authorized announcement date September 29, 2010, invention patent "Modulation Transfer Function Measurement Method and Device for Dynamic Objects", discloses a high-precision and multi-functional dynamic image modulation transfer function measurement device. It also has the structure of a light source, an optical system, and an image sensor, and the light source is also imaged to the surface of the image sensor through the optical system.

Patent No. ZL201010252619.3, authorized announcement date January 11, 2012, invention patent "moving image modulation transfer function measurement device", on the basis of the device disclosed in the previous patent, it further limits the coupling method of the optical lens in the device and The synchronization method of the measurement.

However, the characteristic of these two inventions is that the movement trajectory of the light source is a straight line perpendicular to the optical axis. For an optical system with field curvature, the image will inevitably be defocused during the movement of the light source. If these two inventions are disclosed If the measuring device is directly applied to the present invention, it cannot overcome the problem of image blur caused by defocusing and the problem of image gray value change. This problem will cause a shift in the position of the cutoff frequency, which will affect the accuracy of the measurement result.

Contents of the invention

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 method and device for measuring the lateral magnification of an optical system is proposed. This method can improve the repeatability of measurement results in a small field of view and is more suitable for measuring the lateral magnification of a large distortion optical system; the device can eliminate defocus The impact on the measurement results further improves the repeatability of the measurement results.

The purpose of the present invention is achieved like this:

The method for measuring the lateral magnification of an optical system using a line light source, the steps are as follows:

a. Place a line light source with a length d on the object side, and the direction is parallel to the row or column direction of the image sensor;

b. The image sensor images the line light source to obtain the initial point spread function image; keep the exposure time of the image sensor unchanged, remove the line light source, and the image sensor images the background to obtain the interference image, and the maximum value of the gray value in the interference image as a threshold;

c. From the initial point spread function image obtained in step b, the entire row or column information of the row or column where the line light source image is located is extracted as the initial line spread function image, and the initial line spread function image has n elements; and Correcting the gray value of the pixel whose gray value is smaller than the threshold obtained in the b step to 0 among the n elements to obtain a correction line spread function image, the correction line spread function image has n elements;

or:

In the initial point spread function image obtained in step b, the gray value of the pixel whose gray value is smaller 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 The entire row or column information of the row or column where the image is located is extracted to obtain a correction line expansion function image, and the correction line expansion function image has n elements;

d. Discrete Fourier transform and modulus are performed on the modified line spread function image obtained in the c step to obtain a modulation transfer function image, which has the same number of elements as the modified line spread function image obtained in the c step The number n, that is, n discrete spectral components, are respectively M ₀ , M ₁ , M ₂ , ..., M _n-1 in the order of spatial frequency from small to large. In this order, the modulation transfer function value is the first The modulation transfer function value corresponding to the minimum value is M _i , and its subscript number is i. Combined with the pixel pitch l of the image sensor, the spatial frequency values corresponding to M _i-1 and M _i+1 are respectively: f _min = (i-1)/(nl) and _fmax = (i+1)/(nl);

e. According to the modulation transfer function model MTF(f)=|sinc(πfd′)|, combined with the spatial frequency range f _min and f _max obtained in step d, the value range of the line light source image length is obtained: d _max ′=1/ f _min =nl/(i-1) and d _min '=1/f _max =nl/(i+1);

f. According to the length d of the line light source in step a and the value range of the line light source image length obtained in step e, the value range of the lateral magnification of the optical system is calculated as: β _min =d _min ′/d=nl/((i +1)d) and β _max =d _max '/d=nl/((i-1)d);

g. According to the value range of the lateral magnification of the optical system obtained in step f, divide the lateral magnification of the optical system into N parts on average, namely β ₁ , β ₂ , ..., β _N , where β ₁ = β _min , β _N = β _max ;

该公式所得到的N个值中，最小值所对应的光学系统横向放大率β即为所求。h. Select K from the n modulation transfer function values obtained in step d as comparison data, these K modulation transfer function values are M _K1 , M _K2 , ..., M _KK respectively, and the values obtained in step g The N pixel pitches are respectively substituted into the following formulas:

Among the N values obtained by this formula, the lateral magnification β of the optical system corresponding to the minimum value is the desired value.

An optical system lateral magnification measurement device utilizing a line light source, comprising a line light source, an optical system, and an image sensor, the line light source is imaged to the surface of the image sensor through the optical system, and the optical axis direction of the device is aligned with the image sensor row or column In the plane determined by the direction, the line light source is curved, and any position on the line light source is quasi-focused and imaged on the surface of the image sensor.

The beneficial effects of the present invention are:

1) The measurement method used in the present invention is different from the traditional spatial measurement method. This method takes the line light source as the target to obtain a linear image, searches for the value range of the pixel pitch in the frequency domain, and according to the actual modulation transfer function related to the pixel pitch The coincidence degree between the curve and the theoretical modulation transfer function curve is the best under the condition of least squares, and the lateral magnification of the optical system is calculated by using the search algorithm; The error of the cut-off frequency makes the error between the single measurement results smaller, thereby improving the repeatability of the measurement results;

2) In the measuring device adopted by the present invention, in the plane determined by the optical axis direction of the device and the row or column direction of the image sensor, the line light source is curved, and any position on the line light source is quasi-focused and imaged on the surface of the image sensor ; This feature makes the measured modulation transfer function curve closer to the real curve, and the cutoff frequency position obtained by actual measurement is more accurate, which can further reduce the error between single measurement results and improve the repeatability of measurement results.

Description of drawings

Figure 1 is a schematic diagram of the structure of an optical system lateral magnification measurement device using a line light source

Figure 2 is a plane light path diagram of the lateral magnification measuring device of the optical system using a line light source

Figure 3 is a flow chart of the method for measuring the lateral magnification of an optical system using a line light source

Figure 4 is the initial point spread function image

Figure 5 is the initial line spread function image

Figure 6 is the image of the correction line spread function

In the figure: 1 line light source 2 optical system 3 image sensor

Detailed ways

Specific embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

Fig. 1 is a schematic structural diagram of an optical system transverse magnification measuring device utilizing a line light source, and its planar light path diagram is shown in Fig. 2; The system 2 images the surface of the image sensor 3, and, in the plane determined by the optical axis direction of the device and the image sensor 3 row direction, the line light source 1 is curved, and any position on the line light source 1 is quasi-focused and imaged to the surface of the image sensor 3; wherein, the lateral length of the line light source 1 is 3 mm, and the pixel pitch of the image sensor 3 is 5.6 μm.

The method for measuring the lateral magnification of an optical system using a line light source, the flow chart is shown in Figure 3, and the steps of the method are as follows:

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

b. The image sensor 3 images the line light source 1, as shown in Figure 4, to obtain the initial point spread function image; keep the exposure time of the image sensor 3 unchanged, remove the line light source 1, and the image sensor 3 images the background to obtain an interference image, And the maximum value of the gray value in the interference image is used as the threshold, and the threshold is 10;

c. From the initial point spread function image obtained in step b, extract the entire row information of the line light source image as the initial line spread function image, as shown in Figure 5, and add the gray value in the initial line spread function image The gray value of the pixels smaller than the threshold value obtained in step b is corrected to 0, and the correction line spread function image is obtained, as shown in Figure 6, the correction line spread function image has n=1280 elements;

or:

In the initial point spread function image obtained in step b, the gray value of the pixel whose gray value is smaller 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 whole line information of the row where the image is located to obtain the correction line spread function image, as shown in Figure 6, the correction line spread function image has n=1280 elements;

d. Discrete Fourier transform and modulus are performed on the modified line spread function image obtained in the c step to obtain a modulation transfer function image, which has the same number of elements as the modified line spread function image obtained in the c step The number n=1280, that is, 1280 discrete spectrum components, which are M ₀ , M ₁ , M ₂ ,..., M ₁₂₇₉ according to the order of spatial frequency from small to large, and in this order, the modulation transfer function value is the first The modulation transfer function value corresponding to the minimum value is M ₄₂ , and its subscript number is i=42. Combined with the pixel pitch l=5.6 μm of the image sensor 3, the spatial frequency values corresponding to M ₄₁ and M ₄₃ are obtained: f _min =(i-1)/(nl)=(42-1)/(1280×5.6×10 ^-3 )=5.7199 lp/mm and f _max =(i+1)/(nl)=(42+ 1)/(1280×5.6×10 ^-3 )=5.9989lp/mm;

e. According to the modulation transfer function model MTF(f)=|sinc(πfd′)|, combined with the spatial frequency range f _min ＝5.7199lp/mm and f _max ＝5.9989lp/mm obtained in step d, the image length of the line light source is obtained Value range: 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;

f. According to the length d=3mm of the line light source 1 in the step a and the value range of the line light source image length d _min ′=0.1667mm and d _max ′=0.1748mm obtained in the step e, calculate the 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;

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 length of the line light source image is obtained: d′=1/f= nl/i=1280×5.6×10 ^-3 /42=0.1707mm;

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

g. According to the range of β _min = 0.0556 and β _max = 0.0583 of the lateral magnification of the optical system 3 obtained in step f, divide the lateral magnification of the optical system 3 into N=1000 parts on average, which are β ₁ , β ₂ , . .., β ₁₀₀₀ , wherein, β ₁ =β _min =0.0556, β ₁₀₀₀ =β _max =0.0583;

该公式所得到的N＝1000个值中，最小值所对应的光学系统3横向放大率β即为所求，经计算，β＝0.0558。h. According to the order of 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 to the first maximum value, and does not include the first M ₄₂ obtained in step d, a total of K as comparison data, these K modulation transfer function values are M _K1 , M _K2 , ..., M _KK respectively, and N=1000 optical systems obtained in step g The magnifications are respectively substituted 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 desired value, and after calculation, β=0.0558.

Claims (2)

1. Utilize the optical system lateral magnification measuring method of line light source, it is characterized in that described method step is as follows: a. Place a line light source with a length d on the object side, and the direction is parallel to the row or column direction of the image sensor; b. The image sensor images the line light source to obtain the initial point spread function image; keep the exposure time of the image sensor unchanged, remove the line light source, and the image sensor images the background to obtain the interference image, and the maximum value of the gray value in the interference image as a threshold; c. From the initial point spread function image obtained in step b, the entire row or column information of the row or column where the line light source image is located is extracted as the initial line spread function image, and the initial line spread function image has n elements; and Correcting the gray value of the pixel whose gray value is smaller than the threshold obtained in the b step to 0 among the n elements to obtain a correction line spread function image, the correction line spread function image has n elements; or: In the initial point spread function image obtained in step b, the gray value of the pixel whose gray value is smaller 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 The entire row or column information of the row or column where the image is located is extracted to obtain a correction line expansion function image, and the correction line expansion function image has n elements; d. Discrete Fourier transform and modulus are performed on the modified line spread function image obtained in the c step to obtain a modulation transfer function image, which has the same number of elements as the modified line spread function image obtained in the c step The number n, that is, n discrete spectral components, are respectively M ₀ , M ₁ , M ₂ , ..., M _n-1 in the order of spatial frequency from small to large. In this order, the modulation transfer function value is the first The modulation transfer function value corresponding to the minimum value is M _i , and its subscript number is i. Combined with the pixel pitch l of the image sensor, the spatial frequency values corresponding to M _i-1 and M _i+1 are respectively: f _min = (i-1)/(nl) and _fmax = (i+1)/(nl); e. According to the modulation transfer function model MTF(f)=|sin c(πfd′)|, combined with the spatial frequency range f _min and f _max obtained in step d, the value range of the line light source image length is obtained: d _max ′=1 /f _min =nl/(i-1) and d _min '=1/f _max =nl/(i+1); f. According to the length d of the line light source in step a and the value range of the line light source image length obtained in step e, the value range of the lateral magnification of the optical system is calculated as: β _min =d _min ′/d=nl/((i +1)d) and β _max =d _max '/d=nl/((i-1)d); g. According to the value range of the lateral magnification of the optical system obtained in step f, divide the lateral magnification of the optical system into N parts on average, namely β ₁ , β ₂ , ..., β _N , where β ₁ = β _min , β _N = β _max ; h. Select K from the n modulation transfer function values obtained in step d as comparison data, these K modulation transfer function values are M _K1 , M _K2 , ..., M _KK respectively, and the values obtained in step g The N pixel pitches are respectively substituted into the following formulas:

Among the N values obtained by this formula, the lateral magnification β of the optical system corresponding to the minimum value is the desired value. 2. An optical system transverse magnification measurement device utilizing a line light source, comprising a line light source (1), an optical system (2), and an image sensor (3), and the line light source (1) is imaged to an image by the optical system (2) The surface of the sensor (3), is characterized in that: in the plane determined by the optical axis direction of the device and the row or column direction of the image sensor (3), the line light source (1) is curved, and the line light source (1) Any position on the top is quasi-focused and imaged on the surface of the image sensor (3).

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