CN102607816B - Method and device for measuring optical system lateral magnification by utilizing uniform-speed moving point target - Google Patents

Abstract

The method and device for measuring the transverse magnification of an optical system using a uniformly moving point target belong to the field of metrology equipment characterized by the use of optical methods; the method images the point target in a state of uniform motion to obtain a linear image, and searches for it in the frequency domain The value range of the pixel pitch, and according to the best coincidence between the actual modulation transfer function curve and the theoretical modulation transfer function curve related to the pixel pitch under the least squares condition, the lateral magnification of the optical system is calculated by using the search algorithm; in this device The slider bearing the point target is installed on the first guide rail and the second guide rail. When the controller controls the slider to move at a constant speed on the first guide rail, the controller controls the slider to move on the second guide rail, and the movement in the two directions is phased. Cooperating, the point target is always in-focus and imaged on the surface of the image sensor during the movement process; the lateral magnification of the optical system is measured by the present invention, which is beneficial to reduce the error between single measurement results and improve the repeatability of measurement results.

Description

Measuring method of lateral magnification of optical system using uniform moving point target

technical field

The method and device for measuring the lateral magnification of an optical system using a uniform moving point target belongs to the field of metrology equipment characterized by the use of optical methods, and in particular relates to a point light source that moves in a straight line at a uniform speed as a target, and uses a constant moving image MTF in the frequency domain to measure A method and device for measuring the lateral magnification of an optical system. the

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. the

1. Problems with 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. the

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

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. the

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. the

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. the

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. the

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. the

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. the

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. the

In June 1998, "Optoelectronic 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 height 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. the

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

The following conclusions can be drawn from the statement 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. the

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. the

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. the

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

International Patent Classification No. G01M11/02 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. the

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. the

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. the

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

The purpose of the present invention is achieved like this:

The method of measuring the lateral magnification of the optical system using a uniform moving point target, the steps are as follows:

a. Set the movement speed v of the point target and the exposure time t of the image sensor, and the movement displacement of the point target on the object side can be calculated as: d=v t;

b. Under the parameters in step a, the image sensor images the point target moving along the row or column direction of the image sensor to obtain the initial point spread function image; keep the exposure time t of the image sensor unchanged, remove the point target, and the image sensor Background imaging, get the interference image, and use the maximum value of the gray value in the interference image as the threshold;

c. From the initial point spread function image obtained in step b, the entire row or column information of the point target sweeping through the row or column is extracted as the initial line spread function image, and the gray value in the initial line spread function image is less than The gray value of the pixel of the threshold value obtained in step b is corrected to 0, and the correction line spread function image is obtained, and 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 obtained in step b is corrected to 0, as the corrected point spread function image; and in the corrected point spread function image, the point target Scanning the entire row or column information is extracted as 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 obtained respectively: f _min =(i-1)/(nl) and f _max =(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 range of motion displacement of the point target in the image space is obtained: d _max '=1/f _min =nl/(i-1) and d _min '=1/f _max =nl/(i+1);

f. According to the motion displacement d of the point target in the object space obtained in step a and the value range of the motion displacement of the point target in the image space obtained in step e, the value range of the lateral magnification of the optical system is calculated as: β _min = _dmin /d=nl/((i+1)d) and _βmax = _dmax '/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 lateral magnifications of the N optical systems 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 using a uniform moving point target, including a point target, an optical system, an image sensor, a slider, a first guide rail perpendicular to the optical axis direction, and a controller, and the point target is imaged to an image through the optical system sensor surface; and, the device also includes a second guide rail along the optical axis direction, the slide block bearing point target is installed on the first guide rail and the second guide rail, and when the controller controls the slide block to move at a constant speed on the first guide rail, the control The controller controls the slider to move on the second guide rail, and the movement in the two directions cooperates so that the point target is always in-focus and imaged on the surface of the image sensor during the movement. the

The beneficial effects of the present invention are:

1) The measurement method adopted in the present invention is different from the traditional airspace measurement method. This method takes a point light source as the target, images it under the state of uniform motion of the point target, obtains a linear image, and searches for the value range of the pixel pitch in the frequency domain , and according to the best coincidence between the actual modulation transfer function curve and the theoretical modulation transfer function curve related to the pixel pitch under the condition of least squares, the lateral magnification of the optical system is calculated by using the search algorithm; this feature makes it possible to use a short-length line light source When , a higher cutoff frequency will be obtained, thereby amortizing the error of the cutoff frequency, making the error between the single measurement results smaller, and improving the repeatability of the measurement results;

2) The measuring device that the present invention adopts comprises the second guide rail along the optical axis direction, and the slide block of bearing point target is installed on the first guide rail and the second guide rail, and when the controller controls the slide block to move at a constant speed on the first guide rail, control The controller controls the slider to move on the second guide rail, and the movement in the two directions cooperates so that the point target is always in-focus and imaged on the surface of the image sensor during the movement; this feature makes the measured modulation transfer function curve closer to the real curve , the cut-off 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. the

Description of drawings

Figure 1 is a schematic diagram of the structure of the optical system lateral magnification measurement device using a uniform moving point target

Figure 2 is a flow chart of the method for measuring the lateral magnification of an optical system using a uniform moving point target

Figure 3 is the initial point spread function image

Figure 4 is the initial line spread function image

Figure 5 is the image of the correction line extension function

In the figure: 1 point target 2 optical system 3 image sensor 4 slider 5 first guide rail 6 second guide rail 7 controller

Detailed ways

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

Fig. 1 is a schematic structural diagram of an optical system transverse magnification measuring device utilizing a uniform moving point target; the device includes a point target 1, an optical system 2, an image sensor 3, a slider 4, a first guide rail 5 perpendicular to the optical axis direction, and a controller 7. The point target 1 is imaged onto the surface of the image sensor 3 through the optical system 2; and the device also includes a second guide rail 6 along the optical axis, and the slider 4 carrying the point target 1 is installed on the first guide rail 5 and On the second guide rail 6, when the controller 7 controls the slider 4 to move at a constant speed on the first guide rail 5, the controller 7 controls the slider 4 to move on the second guide rail 6, and the movement in the two directions cooperates to make the point target 1 is always in-focus and imaged on the surface of the image sensor 3 during the movement; the point target 1 is a pinhole with a diameter of 15 μm, and the pixel pitch of the image sensor 3 is 5.6 μm. the

The method for measuring the lateral magnification of an optical system using a uniform moving point target is shown in the flow chart in Figure 2. The steps of the method are as follows:

a. Set the moving speed v=8.5mm/s of the point target 1 and the exposure time t=359ms of the image sensor 3, the movement displacement of the point target 1 on the object side can be calculated as: d=v·t=8.5×359× 10 ^-3 = 3.0515mm:

b. Under the parameters of step a, the image sensor 3 images the point target 1 moving along the image sensor 3 row direction to obtain the initial point spread function image, as shown in Figure 3; keep the exposure time t=359ms of the image sensor 3 No change, remove the point target 1, the image sensor 3 images the background to obtain the interference image, and use the maximum value of the gray value in the interference image as the threshold, and the threshold is 10;

c. From the initial point spread function image obtained in step b, extract the information of the entire row scanned by point target 1 as the initial line spread function image, as shown in Figure 4, and gray the initial line spread function image The gray value of the pixel whose intensity value is less than the threshold obtained in step b is corrected to 0, and the correction line spread function image is obtained, as shown in Figure 5, 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 obtained in step b is corrected to 0, as the corrected point spread function image; and in the corrected point spread function image, the point target The entire row information of the scanned row is extracted as the correction line expansion function image, as shown in Figure 5, the correction line expansion 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 respectively : f _min =(i-1)/(nl)=(42-1)/(1280×5.6×10 ⁻³ )=5.71991p/mm and f _max =(i+1)/(nl)=(42 +1)/(1280×5.6×10 _-3 )＝5.99891p/mm;

e. According to the modulation transfer function model MTF(f)=|sinc(πfd′)|, combined with the spatial frequency range f _min ＝5.71991p/mm and f _max ＝5.99891p/mm obtained in step d, the point target 1 at The value range of the motion displacement of the image square: 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 motion displacement d=3.0515mm of the point target 1 in the object space obtained in the step a and the value range of the motion displacement of the point target 1 in the image space obtained in the e step d _min ′=0.1667mm and d _max ′= 0.1748mm, the value range of the lateral magnification of the optical system 3 is calculated as: β _min =d _min ′/d=nl/((i+1)d)=1280×5.6×10 ^-3 /((42+1) ×3.0515)=0.0546 and _βmax = _dmax '/d=nl/((i-1)d)=1280×5.6× ^10-3/ ((42-1)×3.0515)=0.0573;

g. According to the range of β _min = 0.0546 and β _max = 0.0573 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 , where β ₁ =β _min =0.0546, β _N =β _max =0.0573;

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 3 obtained in step g The horizontal magnification ratios 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 (1)

1. Utilize the optical system lateral magnification measurement method of uniform moving point target, it is characterized in that described method step is as follows: a. Set the motion speed v of the point target and the exposure time t of the image sensor, and the motion displacement of the point target on the object side can be calculated as: d=v·t; b. Under the parameters in step a, the image sensor images the point target moving along the row or column direction of the image sensor to obtain the initial point spread function image; keep the exposure time t of the image sensor unchanged, remove the point target, and the image sensor Background imaging to obtain the interference image, and use the maximum value of the gray value in the interference image as the threshold; c. From the initial point spread function image obtained in step b, the entire row or column information of the point target sweeping through the row or column is extracted as the initial line spread function image, and the gray value in the initial line spread function image is less than The gray value of the pixel of the threshold value obtained in step b is corrected to 0, and the corrected line spread function image is obtained, and the corrected 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 obtained in step b is corrected to 0, as the corrected point spread function image; and in the corrected point spread function image, the point target The entire row or column information is extracted by scanning the row or column, and used as 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 range of motion displacement of the point target in the image space is obtained: d _max '=1/f _min =nl/(i-1) and d _min '=1/f _max =nl/(i+1); f. According to the motion displacement d of the point target in the object space obtained in step a and the value range of the motion displacement of the point target in the image space obtained in step e, the value range of the lateral magnification of the optical system is calculated as: β _min = _dmin '/d=nl/((i+1)d) and _βmax = _dmax '/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 lateral magnifications of the N optical systems 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.