CN102607817B - Method for measuring lateral magnification of optical system - Google Patents

Method for measuring lateral magnification of optical system Download PDF

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CN102607817B
CN102607817B CN201210085061.3A CN201210085061A CN102607817B CN 102607817 B CN102607817 B CN 102607817B CN 201210085061 A CN201210085061 A CN 201210085061A CN 102607817 B CN102607817 B CN 102607817B
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optical system
lateral magnification
line
spread function
function image
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CN102607817A (en
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谭久彬
赵烟桥
刘俭
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Harbin Institute of Technology
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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.

Description

Utilize the optical system lateral magnification measuring method of line source
Technical field
Utilizing the optical system lateral magnification measuring method of line source to belong to adopt optical means is the metering outfit field of feature, relates in particular to a kind ofly to take line source as target, at frequency domain, utilizes line source to look like to measure the method for optical system lateral magnification.
Background technology
Optical system lateral magnification is very important parameter in medical science and precision measurement field, and it not only indicates the technical indicator of optical system, can utilize equally this technical indicator to carry out the precision measurement of other parameter.Yet, how to obtain the lateral magnification of an optical system, be the matter of utmost importance of carrying out this work.
One, optical system lateral magnification measuring method problem
1987 07 month, the publish an article magnification > > of object lens in < < opinion microscope of < < medical physics > >, found the contradiction producing in the lateral magnification experimental formula of object lens in microscope and actual measurement process, although this article does not provide the measuring method of object lens lateral magnification, this contradiction has but been drawn the measurement problem of optical system lateral magnification.
And some follow-up articles all show the necessity that optical system lateral magnification is measured.
1999 03 month, the 1st the 2nd phase of volume of the journal > > of the < < Huangshan Higher Training School discussion > > of < < about lateral magnification in geometrical optics that publish an article, this article has been discussed the mathematic(al) representation of optical system lateral magnification, the applicable elements of the method is the perfect optical system imaging under paraxial condition, and when these conditions do not meet, the formula of summing up herein and the error between actual optical system lateral magnification be not explanation but, more lack for this error, how to measure the explanation of optical system lateral magnification method.
2000 05 month, < < South China Normal University journal (natural science edition) > the 2nd phase of > publish an article < < about the analysis of desirable optical system curve of lateral magnification with use > >, according to the definition of optical system lateral magnification, sum up the computing formula of desirable optical system lateral magnification herein, and draw out lateral magnification-object distance image distance curve, the applicable condition of the method remains perfect optical system paraxial rays, and under non-ideal condition, error between the lateral magnification of pointing out in experimental formula and actual lateral magnification is not explanation but, the necessity of measuring optical system lateral magnification method has more been described.
2002 06 month, the 23rd the 3rd phase of volume of the > > of < < Journal of Jiangxi Institute of Education (natural science) the < < that publishes an article derives object image distance formula and the lateral magnification formula > > of lens under paraxial condition with position phase inversion function, this article be take Fourier optics as basis, utilize the phase tranformation effect of lens to derive image range formula and the optical system lateral magnification formula under paraxial condition, yet, the applicable elements of this piece of article remains the perfect optical system imaging under paraxial approximation condition, there are equally same two pieces of problems that article is identical before.
Because the active demand that exists optical system lateral magnification to measure, so in fields such as medical domain and precision measurements, all have scholar to propose the measuring method of oneself.
2010 09 month, the publish an article mensuration > > of the intrinsic magnification of < < digital X-ray machine of < < Medical Imaging Technology > > the 26th volume supplementary issue 1 provides a kind of assay method of magnification, first this assay method is fixed on small ball on x-ray detector, takes the photograph the diameter that the scale carrying with machine after sheet is measured little spheric projection; Print photo, readding under sheet lamp by divider amount the steel ball size of projection on good photo, and accurately measuring its data with vernier caliper, contrast two groups of wrong differences of data.With vernier caliper, measure equally the actual diameter of corresponding steel ball, can draw two diameter ratios, i.e. x-ray hachure magnification.Because this article is not write by precision measurement field personnel, so the measuring method that article adopts is more ancient, what continue to use is tape measure object height, and this tape measure has certain subjectivity, larger on measurement result impact.
2003 09 month, the 17th the 3rd phase of volume of the journal > > of < < Hebei Vocational Technology Normal College publish an article < < relatively plate method survey magnification of telescope > >, this article has been introduced a kind of new method of optical system lateral magnification, this method is compared with existing Lab of General Physics method therefor, not only principle is simple, data are accurate, and has more operability.Yet this method is appointed the constraint of so not breaking away from classic method, and the judgement of image height is still continued to use to the method that rule reads target length, therefore there is equally the problem of subjectivity.
Yet this problem solves along with the developing and being widely applied to precision measurement field rapidly of CCD, meanwhile, the measuring accuracy of optical system lateral magnification is corresponding being improved also.
1998 06 month, the 25th the 3rd phase of volume of the < < photoelectric project > > < < CCD that publishes an article surveys telescopic system magnification > >, the Method And Principle that this article is introduced is simple, directly utilize image height object height recently to measure the magnification of telescopic system, the method that this article is introduced is compared with classic method, image height no longer accepted scale is measured, but judge by the product of the shared CCD number of pixels of groove and pel spacing, this method has reduced the subjective factor in measuring process, make measurement result more accurate.
2002 03 month, the 22nd the 3rd phase of volume of the < < Physical Experiment > > < < lateral magnification method of publishing an article is determined the basic point > > of complex optics, 2006 08 month, the 25th the 8th phase of volume of the < < College Physics > > < < lateral magnification method of publishing an article is measured the basic point > > of optical system, these two pieces of articles have expanded to a new application by lateral magnification, with it, determine the basic point of complex optics, and draw important conclusion, basic point is the function of optical system lateral magnification.This conclusion illustrates the whether accurate directly relevant to the order of accuarcy of optical system lateral magnification of cardinal point determination, therefore, is necessary precise measuring optical system lateral magnification.And the definition of still continuing to use lateral magnification herein, image height and object height ratio are measured, wherein, the measuring principle of above chapter article is still continued to use in the measurement of image height, according to double slit across number of pixels and the product of pel spacing determine.
To the statement of art methods, can sum up to draw a conclusion, for the measurement problem of optical system lateral magnification, be nothing but to adopt two kinds of methods:
1) utilize the definition of optical system lateral magnification, the ratio of image height and object height is directly measured;
2) particular kind of relationship in certain optical systems according to optical system lateral magnification and certain picture altitude, by the indirect measurement realizing optical system lateral magnification of obtaining of picture altitude.
No matter be any method, all need image height to judge, and the determination methods of present stage have identical technical characterictic:
Utilize image across the number of pixel and the product of pel spacing, obtain the elevation information of image.
Although this technical characterictic can be avoided in classic method with the subjective factor in the process of rule measurement image height, but this method also has the problem of self, because the judgement for number of pixels, it can only be integer judgement, the error of exist at most ± 0.5 pixel of the judgement of each side, the error of two just may exist ± 1 pixels of edge, the size of image is less, and error will be larger.Although can increase in theory the length of line source, by sharing error equally by more pixel, made up, but for large distortion optical system, i.e. the different optical system of enlargement ratio under different visual fields, the length that increases line source can be brought new problem equally:
1) increase target size, may make image that serious deformation occurs in length, in this case, not only can not share error equally, can make on the contrary the error in judgement of number of pixels larger, therefore for large distortion optical system, the method is not suitable for measuring in large field range;
2) for large distortion optical system, ought to be within the scope of each small field of view, accurately measure the lateral magnification under this field range, finally obtain the curve of lateral magnification under different visual fields, but the measuring method adopting due to background technology within the scope of small field of view between single measurement result error larger, therefore large distortion optical system lateral magnification measuring repeatability is low.
Two, optical system lateral magnification measurement mechanism problem
The field tests of international Patent classificating number G01M 11/02 optical property, discloses forming of dynamic image modulation transfer function measuring device by two patents of invention:
Patent No. ZL200810137150.1, at on 09 29th, 2010 Granted publication day, patent of invention < < dynamic target modulation transfer function measurement method and device > >, a kind of dynamic image modulation transfer function measuring device of high-accuracy multifunctional is disclosed, in this device, also there is the structure of light source, optical system and imageing sensor, and be that light source arrives image sensor surface through optical system imaging equally.
Patent No. ZL201010252619.3, at on 01 11st, 2012 Granted publication day, patent of invention < < dynamic image modulation transfer function measuring device > >, on the basis of a upper disclosed device of patent, further define the coupling scheme of optical lens and the method for synchronization of measurement in device.
But the movement locus that these two characteristic feature of an inventions are light sources is perpendicular to the straight line of optical axis, for the optical system that has the curvature of field, in the process of light source motion, will inevitably cause the out of focus of image, if these two the disclosed measurement mechanisms of invention are applied directly in the present invention, cannot overcome problem of image blurring and gradation of image value variation issue that out of focus causes, this problem can cause the locational skew of cutoff frequency, and the accuracy of measurement result is affected.
Summary of the invention
The present invention is exactly for large distortion optical system for above-mentioned existing measuring method, be not suitable for measuring in large field range, and within the scope of small field of view, there is again the problem that lateral magnification measuring repeatability is low, and there is the problem of out of focus in existing measurement mechanism, proposed a kind of measuring method and device of optical system lateral magnification, the method can improve measurement result repeatability within the scope of small field of view, is more suitable for measuring large distortion optical system lateral magnification; This device can be eliminated the impact of out of focus on measurement result, further improves measurement result repeatability.
The object of the present invention is achieved like this:
The optical system lateral magnification measuring method of utilizing line source, step is as follows:
A, the line source that is d in object space placement length, direction is parallel with the row or column direction of imageing sensor;
B, imageing sensor, to line source imaging, obtain initial point spread function image; Keep the imageing sensor time shutter constant, remove line source, imageing sensor, to background imaging, obtains interfering picture, and using the maximal value of gray-scale value in interfering picture as threshold value;
C. in initial point spread function image b step being obtained, line source extracts as full line or the permutation information of place row or column, and as initial line spread function image, this initial line spread function image has n element; And the gray-scale value that gray-scale value in this n element is less than the pixel of b step gained threshold value is modified to 0, and obtaining modified line spread function image, this modified line spread function image has n element;
Or:
In the initial point spread function image that b step is obtained, the gray-scale value that gray-scale value is less than the pixel of b step gained threshold value is modified to 0, as adjusting point spread function image; And by adjusting point spread function image, line source extracts as full line or the permutation information of place row or column, obtains modified line spread function image, this modified line spread function image has n element;
D. modified line spread function image c step being obtained carries out discrete Fourier transformation delivery, obtain modulation transfer function image, this modulation transfer function image has the identical element number n of modified line spread function image obtaining with c step, be n discrete spectrum component, according to spatial frequency order from small to large, be respectively M 0, M 1, M 2..., M n-1, under this order, it is M that modulating transfer function value reaches the corresponding modulating transfer function value of minimal value for the first time i, its lower footnote sequence number is i, the pel spacing l of combining image sensor, obtains M i-1and M i+1corresponding spatial frequency values is respectively: f min=(i-1)/(nl) and f max=(i+1)/(nl);
E. according to modulation transfer function model M TF (f)=| sin c (π fd ') |, the spatial frequency range f obtaining in conjunction with d step minand f max, obtain line source as length span: d max'=1/f min=nl/ (i-1) and d min'=1/f max=nl/ (i+1);
F. the line source obtaining according to a step line source length d and e step is as length span, calculates optical system lateral magnification span to be: β min=d min'/d=nl/ ((i+1) d) and β max=d max'/d=nl/ ((i-1) d);
G. the optical system lateral magnification span obtaining according to f step, is divided into N part by optical system lateral magnification, is respectively β 1, β 2..., β n, wherein, β 1min, β nmax;
H. in n the modulating transfer function value obtaining in d step, choose K data as a comparison, this K modulating transfer function value is respectively M k1, M k2..., M kK, N the pel spacing that g step is obtained is updated to respectively following formula: in the resulting N of this formula value, the corresponding optical system lateral magnification of minimum value β is required.
Utilize the optical system lateral magnification measurement mechanism of line source, comprise line source, optical system, imageing sensor, described line source arrives image sensor surface through optical system imaging, and, in this device optical axis direction and image sensor line or the determined plane of column direction, line source is bending, and on described line source optional position all accurate Jiao be imaged onto image sensor surface.
The invention has the beneficial effects as follows:
1) measuring method that the present invention adopts is different from traditional spatial domain measuring method, the method be take line source and is obtained linear image as target, in frequency domain, find the span of pel spacing, and best according to the actual modulated transfer curve relevant to pel spacing and theoretical modulation transfer function curve registration under least square condition, utilize searching algorithm to calculate optical system lateral magnification; When this feature makes to adopt the short and small line source of length, can obtain higher cutoff frequency, thereby share the error of cutoff frequency equally, make the error between single measurement result less, and then improve measurement result repeatability;
2) measurement mechanism that the present invention adopts is in this device optical axis direction and image sensor line or the determined plane of column direction, and line source is bending, and on described line source optional position all accurate Jiao be imaged onto image sensor surface; This feature makes the modulation transfer function curve measuring more approach true curve, and the cutoff frequency position that actual measurement obtains is more accurate, can further reduce the error between single measurement result, improves measurement result repeatability.
Accompanying drawing explanation
Fig. 1 is the optical system lateral magnification measurement mechanism structural representation that utilizes line source
Fig. 2 is the optical system lateral magnification measurement mechanism optical planar circuit figure that utilizes line source
Fig. 3 is the optical system lateral magnification measuring method process flow diagram that utilizes line source
Fig. 4 is initial line spread function image
Fig. 5 is modified line spread function image
In figure: 1 line source 2 optical system 3 imageing sensors
Embodiment
Below in conjunction with accompanying drawing, the specific embodiment of the invention is described in further detail.
Fig. 1 is the optical system lateral magnification measurement mechanism structural representation that utilizes line source, and its optical planar circuit figure as shown in Figure 2; This device comprises line source 1, optical system 2, imageing sensor 3, described line source 1 is imaged onto imageing sensor 3 surfaces through optical system 2, and, in this device optical axis direction and the determined plane of imageing sensor 3 line direction, line source 1 is bending, and on described line source 1 optional position all accurate Jiao be imaged onto imageing sensor 3 surfaces; Wherein, the lateral length of line source 1 is 3mm, and the pel spacing of imageing sensor 3 is 5.6 μ m.
Utilize the optical system lateral magnification measuring method of line source, as shown in Figure 3, the method step is as follows for process flow diagram:
A, the line source 1 that is d=3mm in object space placement length, direction is parallel with imageing sensor 3 line directions;
B, 3 pairs of line source 1 imagings of imageing sensor, obtain initial point spread function image; Keep 3 time shutter of imageing sensor constant, remove line source 1,3 pairs of background imagings of imageing sensor, obtain interfering picture, and using the maximal value of gray-scale value in interfering picture as threshold value, this threshold value is 10;
C. in initial point spread function image b step being obtained, the full line information that line source picture is expert at extracts, as initial line spread function image, as shown in Figure 4, and the gray-scale value that in initial line spread function image, gray-scale value is less than the pixel of b step gained threshold value is modified to 0, obtain modified line spread function image, as shown in Figure 5, this modified line spread function image has n=1280 element;
Or:
In the initial point spread function image that b step is obtained, the gray-scale value that gray-scale value is less than the pixel of b step gained threshold value is modified to 0, as adjusting point spread function image; And by adjusting point spread function image, the full line information that line source picture is expert at extracts, and obtains modified line spread function image, as shown in Figure 5, this modified line spread function image has n=1280 element;
D. modified line spread function image c step being obtained carries out discrete Fourier transformation delivery, obtain modulation transfer function image, this modulation transfer function image has the identical element number n=1280 of modified line spread function image obtaining with c step, 1280 discrete spectrum components, are respectively M according to spatial frequency order from small to large 0, M 1, M 2..., M 1279, under this order, it is M that modulating transfer function value reaches the corresponding modulating transfer function value of minimal value for the first time 42, its lower footnote sequence number is i=42, the pel spacing l=5.6 μ m of combining image sensor 3, obtains M 41and M 43corresponding spatial frequency values 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;
E. according to modulation transfer function model M TF (f)=| sin c (π fd ') |, the spatial frequency range f obtaining in conjunction with d step min=5.7199lp/mm and f max=5.9989lp/mm, obtains line source as length span: 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. the line source obtaining according to a step line source 1 length d=3mm and e step is as length span d min'=0.1667mm and d max'=0.1748mm, calculates optical system lateral magnification span and 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 modulation transfer function model M TF (f)=| sin c (π fd ') |, the spatial frequency values f=5.8594lp/mm obtaining in conjunction with d step, obtains line source and as length is: d '=1/f=nl/i=1280 * 5.6 * 10 -3/ 42=0.1707mm;
F. the line source obtaining according to a step line source 1 length d=3mm and e step is as length d '=0.1707mm, calculates optical system 3 lateral magnifications to be: β=d '/d=nl/ (id)=1280 * 5.6 * 10 -3/ (42 * 3)=0.0569.
G. the optical system 3 lateral magnification span β that obtain according to f step min=0.0556 and β max=0.0583, optical system 3 lateral magnifications are divided into N=1000 part, be respectively β 1, β 2..., β 1000, wherein, β 1min=0.0556, β 1000max=0.0583;
H. according to spatial frequency order from small to large, n=1280 the modulating transfer function value that d step is obtained is depicted as a curve, chooses on this curve from M 0start to first maximum value, and do not comprise the M that d step obtains 42, data are compared in K conduct altogether, and this K modulating transfer function value is respectively M k1, M k2..., M kK, N=1000 the optical system lateral magnification that g step is obtained is updated to respectively following formula: in the resulting N=1000 of this formula value, the corresponding optical system 3 lateral magnification β of minimum value are required, as calculated, and β=0.0558.

Claims (1)

1. the optical system lateral magnification measuring method of utilizing line source, is characterized in that described method step is as follows:
A, the line source that is d in object space placement length, direction is parallel with the row or column direction of imageing sensor;
B, imageing sensor, to line source imaging, obtain initial point spread function image; Keep the imageing sensor time shutter constant, remove line source, imageing sensor, to background imaging, obtains interfering picture, and using the maximal value of gray-scale value in interfering picture as threshold value;
C. in initial point spread function image b step being obtained, line source extracts as full line or the permutation information of place row or column, and as initial line spread function image, this initial line spread function image has n element; And the gray-scale value that gray-scale value in this n element is less than the pixel of b step gained threshold value is modified to 0, and obtaining modified line spread function image, this modified line spread function image has n element;
Or:
In the initial point spread function image that b step is obtained, the gray-scale value that gray-scale value is less than the pixel of b step gained threshold value is modified to 0, as adjusting point spread function image; And by adjusting point spread function image, line source extracts as full line or the permutation information of place row or column, obtains modified line spread function image, this modified line spread function image has n element;
D. modified line spread function image c step being obtained carries out discrete Fourier transformation delivery, obtain modulation transfer function image, this modulation transfer function image has the identical element number n of modified line spread function image obtaining with c step, be n discrete spectrum component, according to spatial frequency order from small to large, be respectively M 0, M 1, M 2..., M n-1, under this order, it is M that modulating transfer function value reaches the corresponding modulating transfer function value of minimal value for the first time i, its lower footnote sequence number is i, the pel spacing l of combining image sensor, obtains M i-1and M i+1corresponding spatial frequency values is respectively: f min=(i-1)/(nl) and f max=(i+1)/(nl);
E. according to modulation transfer function model M TF (f)=| sinc (π fd ') |, the spatial frequency range f obtaining in conjunction with d step minand f max, obtain line source as length span: d max'=1/f min=nl/ (i-1) and d min'=1/f max=nl/ (i+1);
F. the line source obtaining according to a step line source length d and e step is as length span, calculates optical system lateral magnification span to be: β min=d min'/d=nl/ ((i+1) d) and β max=d max'/d=nl/ ((i-1) d);
G. the optical system lateral magnification span obtaining according to f step, is divided into N part by optical system lateral magnification, is respectively β 1, β 2..., β n, wherein, β 1min, β nmax;
H. in n the modulating transfer function value obtaining in d step, choose K data as a comparison, this K modulating transfer function value is respectively M k1, M k2..., M kK, N the pel spacing that g step is obtained is updated to respectively following formula: in the resulting N of this formula value, the corresponding optical system lateral magnification of minimum value β is required.
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