JP4696261B2 - Spatial frequency characteristic measuring method and spatial frequency characteristic measuring apparatus - Google Patents

Description

The present invention, the spatial frequency characteristic measuring method of the optical system, the optical system spatial frequency characteristic measuring apparatus, on the spatial frequency characteristic measuring device of the spatial frequency characteristic measuring how you and the imaging system of the imaging system.

  An image input / output system such as an optical device or an imaging system in which an optical device and an imaging device are combined is used in various places. Particularly in recent years, with the development of digital image processing, a system that outputs an optical input image as a digital image signal is frequently used.

  In an image input / output system using an optical system such as a lens, such as a scanner, a camera, and other devices for digital input of an image, for example, a spatial frequency called MTF (Modulation Transfer Function) (hereinafter also simply referred to as a frequency). ) Response characteristics have been used for evaluation of optical systems.

  What is important in the MTF measurement is a method for evaluating the contrast of each frequency component. Methods for simply evaluating frequency characteristics (MTF) of imaging systems and the like have been continuously obtained, and various studies have been conducted on how to easily obtain the contrast with high accuracy for a specific frequency component.

  As a method for calculating the contrast, a method for obtaining from the maximum value and the minimum value of the sampled data and a method for obtaining from the peak value of the frequency distribution of the sampled data are common (see, for example, Patent Document 1). There is also a method of obtaining from the integrated value of the waveform of sampled data (see Patent Document 2).

  Both methods are common in that a chart having an arbitrary specific frequency component is prepared as an input pattern, and a contrast value is obtained from an output image obtained by actually capturing the input pattern.

  In a method for obtaining contrast from the maximum value and the minimum value of sampled data, a test pattern having a sine wave luminance distribution is used. This is set so that light and dark are alternated so that a specific frequency is obtained in the direction in which measurement is desired, and that the luminance value is a sine wave lattice. The appearance seems to be a line of alternating bright and dark streaks. It has a specific frequency component in a direction perpendicular to the light and dark streaks.

  The optical output value of the captured image is digitized by, for example, an optical sensor, and the optical output value is sampled by a computer or the like. FIG. 12 shows an example of data sampling. The output value shows a sinusoidal curve in response to the luminance value of the test pattern. The markers I1 to IN are sampled data points, and the output value at this point is acquired as data.

  The sampled data is searched to obtain the maximum output value Imax and the minimum output value Imin. The amplitude B as the contrast is obtained from the difference between the maximum output value Imax and the minimum output value Imin.

  Also in the method of obtaining the contrast from the peak value of the data frequency distribution, the output value data is sampled using a test pattern having a sine wave luminance distribution.

  Next, a frequency distribution of the sampled data is created. FIG. 13 is a graph showing an example of creating a frequency distribution of sampling data. In the case of a test pattern having a luminance distribution of a sine wave, the frequency distribution has peaks at both ends Cmin and Cmax of the amplitude of the sine wave, and the frequency decreases between them. Using this feature, the contrast is obtained with the difference between the peak positions at both ends as the amplitude B as shown in FIG.

In the method of obtaining the contrast from the integrated value of the data waveform in Patent Document 2, the output value is also data-sampled using a test pattern having a sine wave luminance distribution. Next, the output waveform is integrated using the sampling data to obtain the contrast. This utilizes the fact that the absolute value of the AC component of the sine wave is integrated to express the amplitude.
JP 2000-138952 A JP-A-2-24528

  In the method of obtaining the contrast from the maximum value and the minimum value of the data, after sampling the data, the contrast can be easily calculated with almost no effort to search for the maximum output value and the minimum output value. However, the retrieved maximum and minimum values are not true maximum and minimum values, and a considerable number of data is required to increase the accuracy. Further, when there is some noise, the noise is obtained as the maximum value or the minimum value, and a contrast different from the actual case may be obtained.

  In the method of obtaining the contrast from the peak value of the frequency distribution of data, although the effort to obtain the frequency distribution increases, the maximum and minimum values are obtained graphically from the frequency distribution, so it is not easily affected by noise, and the obtained contrast is More stable. However, obtaining graphically leaves ambiguity in position determination. In particular, when the contrast is lowered, the two peaks in the frequency distribution may approach and be unable to identify the difference.

  In the method of obtaining the contrast from the integrated value of the data described in Patent Document 2, all sampling data is used, and accurate contrast measurement can be expected. However, for that purpose, it is required to take a large number n of data at a fine sampling interval and perform a heavy load integration operation. If the n number does not exceed a certain level, good accuracy cannot be expected.

The present invention is to solve these problems, even relatively small number of data sampling, the spatial frequency that can be effectively take advantage of all the data sampled to calculate the contrast of simply and efficiently high precision An object is to provide a characteristic measurement method.

  The object of the present invention can be achieved by the following configurations.

(Claim 1)
An imaging step for forming an image of a test pattern having a predetermined luminance distribution by a test optical system, a sampling step for sampling an optical output value of an image formed by the test pattern, and a sampled optical output value group spatial frequency characteristic measuring method of the optical system, characterized in that it comprises a contrast calculating step of calculating a variance calculation step, a contrast of the target optical system using the calculated variance calculating a variance indicating a distribution.

(Claim 2)
A high-luminance block output measuring step of forming an image of a high-luminance block pattern having a luminance value equivalent to the maximum luminance value in the test pattern with the test optical system and obtaining an optical output value of the imaged high-luminance block pattern And a low-brightness block output that images a low-brightness block pattern having a luminance value equivalent to the minimum luminance value in the test pattern by the test optical system and obtains an optical output value of the formed low-brightness block pattern The contrast calculated in the contrast calculation step is normalized using the measurement step and the optical output value acquired in the high luminance block output measurement step and the optical output value acquired in the low luminance block output measurement step. spatial frequency characteristic measurement of an optical system according to claim 1, characterized in that it comprises a normalization step Law.

(Claim 3)
The variance calculating step calculates a variance of the optical output value group sampled in the sampling step, and the contrast calculating step multiplies the square root of the variance calculated in the variance calculating step by a constant. The method of measuring a spatial frequency characteristic of an optical system according to claim 1, wherein the contrast of the optical system is calculated.

(Claim 4)
Sampling means for sampling the test pattern having a predetermined luminance distribution, the optical output value of the test pattern imaged by the test optical system, and the variance indicating the distribution of the sampled optical output value group a variance calculating means for, optical spatial frequency characteristic measuring apparatus characterized by having a contrast calculating means for calculating a contrast of the target optical system using the calculated variance.

(Claim 5)
In a spatial frequency characteristic measuring method of an imaging system having an optical system and an imaging device that images an image formed by the optical system, an imaging step of imaging a test pattern having a predetermined luminance distribution, and an output from the imaging device wherein the output value when the test pattern captured that, a sampling step of sampling, the variance calculation step of calculating the variance indicating the distribution of the output value group obtained by sampling, the contrast of the imaging system using the calculated variance A method for measuring a spatial frequency characteristic of an imaging system, comprising: calculating a contrast.

(Claim 6)
In a spatial frequency characteristic measuring apparatus for measuring the contrast of an imaging system having an optical system and an imaging device that captures an image formed by the optical system, a test pattern having a predetermined luminance distribution and output from the imaging device the output value obtained when imaging the test pattern, calculating a sampling means for sampling, the variance calculating means for calculating a variance indicating the distribution of the output value group obtained by sampling, the contrast of the imaging system using the calculated variance A spatial frequency characteristic measuring apparatus for an imaging system, comprising:

(Claim 7)
In a spatial frequency characteristic measurement method for measuring a spatial frequency characteristic of an imaging system having an optical system and an imaging element that captures an image formed by the optical system, a plurality of test patterns each having a luminance distribution with different spatial frequencies An imaging step for imaging, a sampling step for sampling the output value when the test pattern output from the imaging device is imaged for each test pattern, and a sampled output value group for each test pattern A variance calculating step for calculating variance, a contrast calculating step for calculating the contrast of the imaging system by multiplying a square root of the calculated variance for each test pattern, and a maximum luminance value in the test pattern; High-intensity block pattern with equivalent luminance value A high-luminance block output measurement step for obtaining an output value of the high-luminance block pattern, and imaging a low-luminance block pattern having a luminance value equivalent to the minimum luminance value in the test pattern, and outputting the low-luminance block pattern A low-luminance block output measurement step for acquiring a value, and for each test pattern, using the output value acquired in the high-luminance block output measurement step and the output value acquired in the low-luminance block output measurement step, the contrast A normalization step for normalizing the contrast calculated in the calculation step, and a spatial frequency characteristic based on the contrast of the imaging system in each test pattern normalized in the normalization step and the spatial frequency of each test pattern Including a spatial frequency characteristic calculation step. Spatial frequency characteristic measuring method of the imaging system, characterized in that.

According to the invention described in claim 1 or claim 4, by efficiently using all the sampled data values in the form of calculating the variance , the efficiency can be reduced with a smaller number of sampling data, regardless of the magnitude of the contrast. The contrast of the optical system with good accuracy can be obtained.

  According to the second aspect of the present invention, since the calculated contrast is normalized using the output value of the high luminance block pattern and the output value of the low luminance block pattern, the sine of the frequency is changed each time the measurement frequency is changed. It is not necessary to calculate a 100% response output (that is, a parameter for normalization) of a wave or a rectangular wave, and the normalized contrast for each frequency can be obtained efficiently.

According to the invention described in claim 3, since the dispersion uses a commonly used dispersion and the contrast can be obtained directly from the dispersion, the influence of an abnormal value, etc. can be simply and efficiently. The contrast can be obtained.

According to the invention described in claim 5 or 6, even in the entire input / output system including the imaging system, the sampling data can be reduced by effectively using all the sampled data values in the form of calculating the variance. The contrast of the system as a system can be easily and efficiently calculated regardless of the size of the contrast.

According to the invention described in claim 7, even in the entire input / output system including the imaging system, the data value sampled in the form of calculating the variance is effectively used, and the measurement frequency is changed whenever the measurement frequency is changed. Since it is not necessary to calculate the 100% response output of frequency sine wave or square wave (ie, parameter for normalization), normalization for each frequency can be performed efficiently and accurately with a smaller number of sampling data. Therefore, the frequency characteristics of the system can be easily calculated.

  As a first embodiment according to the present invention, as an example, a method for calculating a spatial frequency characteristic (MTF) of an imaging system that is an imaging system including an optical device that is an optical system and an imaging device that is an imaging means, This will be described below.

FIG. 1 is a diagram illustrating a configuration example of an imaging system that is an imaging system according to the present invention and a spatial frequency characteristic measuring apparatus that measures spatial frequency characteristics (hereinafter simply referred to as frequency characteristics) of the imaging system.

  Reference numeral 11 denotes a test pattern, which may be a real scene or an image recorded on a recording medium such as paper by an imaging system. In this embodiment, it is an image on a recording medium. An optical device 12 functions as an optical system. Reference numeral 13 denotes an image pickup element that functions as an image pickup unit, and converts an optical image generated by the optical device 12 into an electric signal. An image output unit 14 receives an electrical signal from the image sensor 13 and outputs it as a digital output image signal. In other words, the optical device 12, the image sensor 13, and the image output unit 14 cooperate to form the imaging system 1, and function as an imaging system.

The MTF measurement unit 15 includes a CPU (Central Processing Unit) (not shown), a work memory, and the like, reads a program stored in a storage unit (not shown) into the work memory, and outputs the program from the image output unit 14 according to the program. The image signal is taken in and the MTF of the imaging system 1 is calculated. In other words, the test pattern 11 and the MTF measurement unit 15 cooperate to function as an imaging system spatial frequency characteristic measurement apparatus according to the present invention.

  In addition, as shown in the block diagram of FIG. 3, the MTF measurement unit 15 includes a sampling unit 151, a statistic calculation unit 152, a contrast calculation unit 153, a high luminance block output measurement unit 154, a low luminance block output measurement unit 155, a contrast Functions as normalization means 156 and spatial frequency characteristic calculation means 157 are provided.

  The sampling means 151 samples the output value of the captured rectangular wave or sine wave output image two-dimensionally for each spatial frequency.

  The statistic calculation means 152 calculates the variance of the output value group sampled by the sampling means 151 for each spatial frequency.

  The contrast calculation unit 153 calculates the contrast of the imaging system for each spatial frequency by multiplying the square root of the variance calculated by the statistic calculation unit 152 by a constant for each spatial frequency.

  The high luminance block output measuring means 154 acquires the output value of the imaged high luminance block pattern. The low luminance block output measuring unit 155 acquires the output value of the captured low luminance block pattern.

  The contrast normalization unit 156 uses the output value acquired by the high luminance block output measurement unit 154 and the output value acquired by the low luminance block output measurement unit 155 for each spatial frequency, and uses the contrast calculation unit 153. Normalize the contrast calculated in.

  The frequency characteristic calculation unit 157 calculates a spatial frequency characteristic (MTF) based on the contrast for each spatial frequency normalized by the contrast normalization unit 156.

  Returning to FIG. 1, the MTF measurement of the imaging system 1 will be described.

  First, the test pattern 11 is set on the optical device 12 or arranged in an optically captureable positional relationship, and is connected to the optical device 12 via the optical device 12 by an appropriate starting means (not shown). An image is formed on the combined image sensor 13. The image sensor 13 converts an optical image on the image sensor into an electric signal. The image output unit 14 receives the electrical signal from the image sensor 13 and outputs it as a digital image signal capable of image processing.

  Although the optical device 12 is represented by a single lens in FIG. 1, it is often configured using a plurality of lens groups. Further, an optical conversion device other than a lens may be used, and the optical method is not limited to an optical method as long as an input image can be captured on an image sensor. As the image sensor 13, a photoelectric conversion device using a CCD is used. Any device that can convert an optical image or an image formed on an image sensor into an electrical signal may be used. Further, the signal conversion in the image sensor 13 may be performed two-dimensionally in parallel or in series. The image output unit 14 digitizes the output image to facilitate digital image processing. In the image output unit 14, sampling of an image signal may be performed instead of the sampling unit 151 of the MTF measurement unit 15.

  The test pattern 11 for calculating the frequency characteristic (MTF) will be described. The frequency characteristic can be obtained by obtaining the contrast of the output image for each frequency and normalizing the image contrast for each frequency.

  Therefore, in order to obtain the contrast value for each frequency component, a test pattern having a predetermined frequency component is prepared as a test pattern.

  As a test pattern having a specific frequency component, a sine wave lattice pattern (hereinafter also referred to as a sine wave pattern) is often used. The frequency of the sine wave is specified by the wavelength (light-dark alternation cycle) on the test pattern. Further, since the image is two-dimensional, at least a plurality of sinusoidal test patterns whose directions are orthogonal to each other are required.

  In addition, since a chart can be easily created, a lattice pattern using a rectangular wave (hereinafter also referred to as a rectangular wave pattern) is often used. In the case of a rectangular wave, the frequency component included in the waveform is not limited to a specific frequency, and attention is required because it has a higher-order frequency component superimposed on the main frequency. However, since high-order frequency components often have negligible responses, they can be used by paying attention to them and performing appropriate corrections. The need for an input pattern of a plurality of rectangular waves whose directions are orthogonal is the same as in the case of a sine wave.

  FIG. 2A shows an example of the test pattern 11 using a rectangular wave pattern. FIG. 2B shows the luminance distribution of the test pattern 11 using a rectangular wave pattern.

  In the test pattern 11, the high luminance portion 22 and the low luminance portion 21 are alternately replaced with each other in a certain direction to form a lattice. The widths of the high luminance part 22 and the low luminance part 21 were set to 1 / 2u so that the main frequency of the test pattern 11 was u. The black and white ratio of the high luminance part 22 and the low luminance part 21 is 1: 1. When the rectangular wave pattern is Fourier-expanded, it can be seen that it further has higher-order frequency components such as 3u, 5u,... (Details will be described later).

  In this embodiment, a case will be described in which a contrast is obtained using a rectangular wave test pattern and a frequency characteristic (MTF) is obtained.

  As the test pattern, another block pattern image including a low-frequency solid image is used. This is used to obtain a parameter used for contrast normalization described later. Each is a solid pattern including a high luminance portion block and a low luminance portion block corresponding to the high luminance portion and the low luminance portion of the rectangular wave pattern. Details of normalizing the response contrast of each frequency component by using the response to the extremely low frequency component will be described later with reference to FIG.

  From the actual output image using the imaging system and the test pattern, the MTF measurement unit 15 performs normalization parameter calculation, contrast calculation, and frequency characteristic calculation. Before describing the actual procedure of each process, the formulas used in each process and the derivation of those formulas will be described.

  Equations necessary in the process of calculating the contrast for the sine wave or rectangular wave with the frequency u are as follows.

(A) When a sine wave pattern (or rectangular wave pattern) having a spatial frequency u is input and the same sine wave output data is acquired, the output data is sampled and the output value variance σ ² as a statistic is calculated. A formula for obtaining the output amplitude B.

  (B) When the high luminance and low luminance portion block images having the same luminance values as the high luminance portion and low luminance portion of the sine wave pattern are input and the output values of the high luminance portion and low luminance portion are acquired, the output values To obtain the input amplitude A ′ as a parameter for normalizing the contrast (and, if a rectangular wave pattern is used instead of the sine wave pattern, it is further converted to a sine wave to obtain the input amplitude A).

  (C) A mathematical expression for obtaining a normalized contrast from the output amplitude B and the input amplitude A ′ or A for each frequency.

The mathematical formula for obtaining the output amplitude B from the output value variance σ ² used in the contrast calculation process of (a) will be described below.

  First, for a sinusoidal output, it is shown that the output amplitude can be calculated from the variance as a statistic, and Equation (3) is derived.

  A sinusoidal output y (θ) = Bsinθ with amplitude B is sampled independently of the waveform to obtain N pieces of output value data. Since sampling is independent of θ, it may be considered that sampling is performed uniformly over a range of 0 ≦ θ <2π that is a period.

  A frequency distribution is taken for the N sampling data. The frequency n (y) for each output value y is proportional to the inverse dθ / dy of the slope of the output y (θ).

  As shown in Equation (1), when frequency n (y) = dθ / dy, a frequency distribution as shown in the graph of FIG. 4 is obtained.

n (y) = dθ / dy (1)
The horizontal axis in FIG. 4 is the output value y of the output image. If the amplitude of the sine wave of the output image is B, the output value y is limited to a range from -B to + B. The vertical axis represents the frequency n (y) of each output value.

  The expected value of the distribution variance is represented by the following formula (2) (the integration range is from -B to + B).

Solving this σ ² = B ^2/2, and the equation (3) is derived.

Equation (3) is independent of the frequency u of the sine wave used. Using this, the output amplitude B (u) is calculated from the variance σ ² (u).

  Next, consider a case where a rectangular wave pattern having a spatial frequency u is used instead of a sine wave pattern. In that case, the rectangular wave pattern should contain a higher-order frequency component in addition to the main frequency u. However, if the response of the higher-order frequency of the frequency 3u or higher can be ignored, the output amplitude B is equal to the main frequency u. It can be considered that it consists only of components, and the above formula (3) can be used as it is.

  Regarding the mathematical formula for obtaining the input amplitude A ′ or A as the parameter for contrast normalization from the output values of the high luminance part, the low luminance part, and each block pattern used in the normalization parameter calculation process of (b), Explained.

  It shows that the input amplitude A ′ or A for normalization can be calculated from the output values of the high luminance part and low luminance part block patterns, and the equations (4) and (7) are derived. The input amplitude represents an output amplitude when it is assumed that 100% output is obtained with respect to a sine wave input. In other words, it is the maximum contrast that can be expected and is usually smaller in amplitude, that is, 100% or less.

  Considering that the block pattern is composed of only extremely low frequency components, the output amplitude when assuming that 100% output is obtained is calculated from the output of the block pattern (usually the response is 100% when the frequency u is close to zero). Nearer, the higher the frequency, the lower the response).

  The output values of the high luminance portion and the low luminance portion of the block pattern are Lw and Lb (Lw> Lb), the amplitude of the block pattern is A ′, and the input amplitude A ′ can be expressed by the following equation (4). This is what the block pattern is regarded as a sine wave whose frequency is very close to zero, and is called amplitude.

A ′ = (Lw−Lb) / 2 (4)
If the output values of the high luminance part and the low luminance part become the same Lw and Lb as the block pattern in response to 100% of the sine wave output of the frequency u, the same equation (4) can be applied. That is, the amplitude of the sine wave output when assuming 100% response to the sine wave input of the frequency u can also be expressed as A ′ = (Lw−Lb) / 2. This does not depend on the frequency u.

  Let us consider a case where a rectangular wave pattern with a spatial frequency u is used as an input instead of a sine wave. In this case, as described above, the rectangular wave pattern includes high-order frequency components in addition to the main frequency u. When the rectangular wave F (x) having the frequency u is Fourier-expanded, the following equation (5) is obtained.

  In equation (5), the first term is a sine wave with a frequency u, the second term is a sine wave with a frequency 3u, the third term is a sine wave with a frequency 5u, and a term consisting of a higher order sine wave is omitted, but omitted. is doing.

  Therefore, if it is considered that the response can be ignored for high-order frequency components of frequency 3u or higher, the output can be expressed as in the following equation (6).

F (x) = (4 / π) sin2πux (6)
That is, it can be regarded as a sine wave having an output amplitude of 4 / π at the frequency u. This has an amplitude of 4 / π times that of the original rectangular wave.

  Assuming that the response of the rectangular wave with the main frequency u is 100%, it can be considered that the amplitude can be expressed as in Expression (4) using the input amplitude of the block pattern as it is.

A ′ = (Lw−Lb) / 2 (4)
Therefore, when the output corresponding to the response of the rectangular wave of the main frequency u is only the sine wave component of the frequency u, it cannot be said that the response is 100% unless the input amplitude is expressed as in Equation (7). become.

A = (4 / π) (Lw−Lb) / 2 (7)
Therefore, when a rectangular wave pattern with a spatial frequency u is used, Equation (7) is used as a parameter for contrast normalization. This equation (7) also does not depend on the frequency u.

  A mathematical expression for obtaining the normalized contrast from the output amplitude B and the input amplitude A ′ or A for each frequency used in the frequency characteristic calculation process of (c) will be described below.

  The normalized contrast is calculated from the output amplitude B and the input amplitude A ′ or A, and equations (10) and (11) for obtaining the frequency characteristics are derived.

  FIG. 5 shows the relationship between the input amplitude and the output amplitude. A dotted line 51 represents an output when it is assumed that 100% response is made to the rectangular wave input. The amplitude of the output is A (A ′ when the input is a sine wave), which is referred to as the input amplitude. A solid line 52 represents an actual output for a rectangular wave input. The output amplitude is B, which is referred to as output amplitude.

  If the frequency characteristic at the frequency u is MTF (u), this is the normalized contrast at the frequency u, which can be expressed by Equation (8).

MTF (u) = output amplitude (u) / input amplitude (8)
Here, contrast is expressed by amplitude. Further, by assuming that the virtual output amplitude when assuming 100% response is the parameter of division as the input amplitude, the response of the output to the frequency u can be expressed as a percentage.

  When a sine wave pattern having a spatial frequency u is used, it can be expressed by Equation (9) from the output amplitude B already obtained by Equation (3).

  The frequency characteristic MTF (u) can be calculated according to Equation (10) using the output amplitude B (u) and the input amplitude A ′.

  Further, when a rectangular wave pattern having a spatial frequency u is used, the output amplitude B (u) and the input amplitude A that have already been obtained can be used to calculate using the formula (11).

  The above is a description of formulas used in the process of calculating contrast and obtaining frequency characteristics, and derivation of those formulas. In the following, a procedure for specifically processing a digital output image using the above-described mathematical formula, calculating a contrast for a sine wave of a frequency u or a rectangular wave, and finally obtaining a frequency characteristic (MTF), This will be described with reference to FIGS. 6, 7, and 8.

  FIG. 6 is a flowchart showing a flow of calculating the frequency characteristic (MTF). With reference to FIG. 6, a rough flow of calculating the frequency characteristic (MTF) will be described.

  When the frequency characteristic calculation process is started, first, a normalization parameter calculation process S61 described later is performed. This is a process using a block pattern and may be performed independently of the process for each frequency using the next rectangular wave pattern (steps S62 to S64). However, since the processing result of step S61 is used in the step of calculating and normalizing the contrast for each frequency (S63), it is necessary to perform it in advance.

  Next, the process moves to each frequency. In step S62, the frequency setting is sequentially updated. Next, contrast calculation processing S63 described later is performed with the updated set frequency.

  When the process of step S63 is completed, it is determined in step S64 whether all frequency settings scheduled for measurement have been completed. If it is determined that all the scheduled frequency settings have not yet been completed (step S64: NO), the process returns to step S62, and the next scheduled measurement frequency is set. If it is determined in step S64 that all scheduled frequency settings have been completed (step S64: YES), the process proceeds to step S65, and the frequency characteristic (MTF) is calculated using the result of the contrast calculation process S63 at each frequency. The frequency characteristic calculation process is finished.

  Further, in the processing procedure of this embodiment, in order to calculate the frequency characteristics, the set frequency is updated and the test pattern is sequentially input. For example, a plurality of test patterns are collected into one sheet and imaged once. It is also possible to input / output a plurality of test patterns.

  Next, details of the normalization parameter calculation processing for each set frequency will be described with reference to FIG. FIG. 7 is a flowchart showing the flow of the normalization parameter calculation process for normalizing the contrast at each set frequency, and is a detailed flow of the normalization parameter calculation process S61 of FIG.

  When the normalization parameter calculation processing is started, first, in step S71, an input block pattern chart is prepared. The chart image is set so as to include a high luminance portion and a low luminance portion having the same luminance value as the high luminance portion and low luminance portion of the rectangular wave pattern of each frequency for input as a block pattern.

  In step S72, the test pattern (block pattern) is input. Through the input / output process in the imaging system already described, a block pattern converted into a digital signal is output in step S73.

  The next step S74 is a high luminance block output measuring step and a low luminance block output measuring step. In step S74, the output values of the high luminance block pattern and the low luminance block pattern of the block pattern output image are obtained by appropriately sampling. The output values of the high luminance part and the low luminance part are Lw and Lb (Lw> Lb), respectively.

  Next, in step S75, the block image amplitude A 'is obtained from Lw and Lb obtained in step S74 according to Equation (4).

A ′ = (Lw−Lb) / 2 (4)
In the present embodiment, in consideration of normalizing the contrast of each frequency component, the contrast is expressed by the amplitude of a sine wave. Accordingly, the block image is also regarded as an extremely low frequency image, and half of the difference between Lw and Lb corresponding to the amplitude is called the block image amplitude to express the contrast.

  Next, in step S76, by multiplying the amplitude A ′ of the block image obtained in step S75 by 4 / π as a parameter for normalizing the contrast with respect to the output image of each frequency component, according to equation (7). Then, the input amplitude A of the rectangular wave image is obtained.

A = (4 / π) (Lw−Lb) / 2 (7)
The input amplitude A is an output amplitude when the response is the same as that of the block image, that is, a response of 100%, and is referred to as an input amplitude as a parameter for normalizing the contrast. A sine wave image having the same response as the block image has the same amplitude A ′ as the block image, but in order to have the same response as the rectangular wave image, that is, to have the same amplitude A ′, the sine wave included in the rectangular wave The wave must have the input amplitude A described above.

  In this embodiment, since the contrast is calculated using the rectangular wave pattern, the input amplitude A obtained in step S76 is used as a parameter for normalizing the contrast. When a sine wave chart is used as the input pattern, this step S76 is omitted, and the block image amplitude A ′ obtained in step S75 is regarded as the input amplitude A as it is and is used as a parameter for normalizing the contrast. That's fine.

  This completes the normalization parameter calculation processing. The input amplitude obtained by this processing represents the amplitude of the sine wave output when it is assumed that the same response as that of the block image is obtained. Normalize the response (contrast). The calculation result of this parameter is used for normalization in the contrast calculation process S63.

  Next, the details of the contrast calculation process for each set frequency will be described with reference to FIG. FIG. 8 is a flowchart showing the flow of contrast calculation processing for each set frequency, and is a detailed flow of contrast calculation processing S63 in FIG.

  When the contrast calculation process is started, first, in step S81, a rectangular wave pattern having the set frequency u updated in step S62 as a main frequency component is prepared.

  Next, in step S82 (imaging step), a rectangular wave pattern having the set frequency u is input. Through the input / output process in the imaging system already described, in step S83, an image converted into a digital signal is output (imaging step). The contrast of this output image is obtained as follows.

  Next, in step S84, the image output in step S83 is sampled (sampling step).

  FIG. 9 shows the sampling state of the output image. In the output image, light and dark are reproduced in a lattice shape, and FIG. 9 is a cross-sectional view taken along a direction in which the lattice-like output value has a frequency component. In FIG. 9, the sampled positions are indicated by markers (I1 to In). The output value at this marker position is used as statistic calculation data.

  The sampling interval may be appropriately determined according to the frequency. In the case of the frequency u, it is desirable that the frequency u is sufficiently smaller than 1 / 2u so that it does not have a common divisor. Further, the sampling position may be determined at random. The greater the number of samplings, the higher the reliability of the statistics, so the reliability may be set in consideration of the purpose.

Next, in step S85, the variance σ ² (u) is obtained from the data sampled in step S84 (statistic calculation step). The variance as a statistic can be calculated as the root mean square of the sampled output values, as is well known.

Next, in step S86, the output amplitude B (u) is obtained from the variance σ ² (u) obtained in step S85 according to the equation (9) (contrast calculation step).

If the output image can be regarded as a sine wave shape, when the output value is y = Bsin θ, y ² is integrated with θ, and normalized by integration with θ, the variance is obtained, thereby obtaining Equation (9).

  Next, in step S87, normalization is performed on the output amplitude B (u) obtained in step S86 (normalization step). The normalization step assumes the calculation of a frequency response, and this normalization process is not necessary for the purpose of measuring the best focus position or adjusting the focus.

  In the normalization parameter calculation processing in step S61, the normalization input amplitude A has already been obtained. As shown in Equation (11), the normalized contrast (in this embodiment, the MTF value for a specific frequency) is obtained by dividing the output amplitude B (u) obtained in step S86 by this input amplitude A. it can.

  The input amplitude A is assumed that the output sine wave image with respect to the rectangular wave input image of each higher frequency component has the same response with reference to the output value for the very low frequency component, that is, the block pattern, The amplitude is the input amplitude A. Usually, the response decreases as the frequency becomes higher. Therefore, the virtual input amplitude A is the maximum response that can be expected in the system, and the output amplitude B is smaller than that.

  In the present embodiment, the contrast is calculated using the rectangular wave pattern. However, when the sine wave chart is used as the input pattern, as described above, the amplitude A ′ of the block image obtained in step S61 is used as it is. Assuming that the input amplitude is A, normalized contrast (in this embodiment, an MTF value for a specific frequency) may be obtained as shown in Equation (10).

  This is the end of the contrast calculation process. What is obtained in this process is the normalized contrast for each frequency component, and in step S65, which is a frequency characteristic calculation step, this result is collected as frequency characteristics for all measured frequency components.

  FIG. 10 shows an example in which the final frequency characteristic (MTF) is graphed. The horizontal axis represents the frequency u in units of mm / mm, and the vertical axis represents the MTF with respect to the frequency u in percent. A curve S indicates a frequency characteristic of the imaging system. The frequency characteristic represented by the curve S is normalized so that the frequency is zero and the MTF is 100%. The reason why the data of the curve S is not present in the low frequency region is that the data is limited to a frequency at which the response to a higher-order frequency of 3u or more can be ignored. It is estimated to be connected to MTF 100% at a frequency of zero, and is indicated by a dotted line.

  As described above, according to the embodiment of the present invention, by using all the sampled data values effectively by using a commonly used statistic called variance, the magnitude of contrast can be reduced with a smaller number of sampled data. Nevertheless, efficient, simple, and accurate contrast can be obtained, and the target system can be applied to the entire input / output system including the optical system alone or the imaging system. This is particularly effective for calculating frequency characteristics such as MTF.

  Various variations of the apparatus for realizing the present invention can be envisaged. As long as the embodiment of the present invention conforms to the spirit of the method of the present invention, the modified form includes the modified embodiments.

  As a second embodiment according to the present invention, a method for calculating the MTF of an optical device which is an optical system will be described below as an example.

FIG. 11 is a diagram illustrating a configuration example of an MTF measurement apparatus that measures the MTF of an optical device that is an optical system according to the present invention. In addition, the same code | symbol is attached | subjected to the same component as what was demonstrated in 1st Embodiment. The difference between the present embodiment and the first embodiment is that the measurement target is a single optical device 12 instead of the imaging system 1, and instead of the imaging device 13 of the imaging system, a sampling means is used. This is a point having an image sensor 13a that functions as a part. That is, the test pattern 11, the image sensor 13a, and the MTF measurement unit 15 cooperate to function as an optical system spatial frequency characteristic measurement apparatus according to the present invention. The other points except for the above differences are the same as those in the first embodiment including the operation, and the detailed description thereof is omitted.

It is a figure which shows the structural example of the spatial frequency characteristic measuring apparatus of the imaging system which concerns on this invention. It is a figure which shows an example of the test pattern which concerns on this invention. FIG. 2 is a block diagram illustrating a configuration example of an MTF (frequency characteristic) measurement unit in FIG. 1. It is a figure which shows the frequency distribution of the output value of a sine wave-like output image output from an imaging system. It is a figure which shows a response | compatibility of an input amplitude and an output amplitude about an imaging system. It is a flowchart which shows the flow which calculates the frequency characteristic (MTF) based on the method of this invention. It is a flowchart which shows the flow of the parameter calculation process for normalization for normalizing the contrast in each setting frequency based on the method of this invention. It is a flowchart which shows the flow of the contrast calculation process with respect to each setting frequency based on the method of this invention. It is a figure which shows the state of sampling of the output image output from an imaging system based on the method of this invention. It is a figure which shows the example which put together about all the measured frequency components based on the method of this invention, and was graphed as a frequency characteristic (MTF). It is a figure which shows the structural example of the frequency characteristic measuring apparatus of the optical device single-piece | unit based on this invention. It is a figure which shows the data sampling of contrast calculation by a prior art example. It is a figure which shows contrast calculation using the frequency distribution by a conventional example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Imaging system 11 Input pattern 12 Optical device 13, 13a Image pick-up element 14 Image output part 15 MTF measurement part 151 Sampling means 152 Statistics calculation means 153 Contrast calculation means 154 High brightness block output measurement means 155 Low brightness block output measurement means 156 Contrast Normalizing means 157 Spatial frequency characteristic calculating means

Claims (7)

An imaging step of forming an image of a test pattern having a predetermined luminance distribution by a test optical system;
A sampling step of sampling an optical output value of an image formed by the test pattern;
A variance calculation step of calculating a variance indicating a distribution of the sampled optical output value group,
A method of measuring a spatial frequency characteristic of the optical system, comprising: a contrast calculation step of calculating a contrast of the optical system to be measured using the calculated dispersion . A high-luminance block output measuring step of forming an image of a high-luminance block pattern having a luminance value equivalent to the maximum luminance value in the test pattern with the test optical system and obtaining an optical output value of the imaged high-luminance block pattern When,
Low-luminance block output measurement step of imaging a low-luminance block pattern having a luminance value equivalent to the minimum luminance value in the test pattern by the test optical system and obtaining an optical output value of the imaged low-luminance block pattern When,
A normalizing step for normalizing the contrast calculated in the contrast calculating step using the optical output value acquired in the high luminance block output measuring step and the optical output value acquired in the low luminance block output measuring step; The method for measuring a spatial frequency characteristic of an optical system according to claim 1. The variance calculating step calculates a variance of the optical output value group sampled in the sampling step,
3. The optical system according to claim 1, wherein the contrast calculating step calculates a contrast of the optical system to be measured by multiplying a square root of the dispersion calculated in the dispersion calculating step by a constant. Spatial frequency characteristic measurement method. A test pattern having a predetermined luminance distribution;
Sampling means for sampling the optical output value of the test pattern imaged by the test optical system;
A variance calculating means for calculating a variance indicating a distribution of the sampled optical output value group,
An apparatus for measuring a spatial frequency characteristic of an optical system, comprising: contrast calculation means for calculating a contrast of the optical system to be measured using the calculated dispersion . In a spatial frequency characteristic measuring method of an imaging system having an optical system and an imaging device that captures an image formed by the optical system,
An imaging step of imaging a test pattern having a predetermined luminance distribution;
A sampling step of sampling an output value when the test pattern output from the image sensor is imaged;
A variance calculation step of calculating the variance indicating the distribution of the output value group sampled,
Spatial frequency characteristic measuring method of the imaging system, characterized by using the calculated variance and a contrast calculating a contrast of the imaging system. In a spatial frequency characteristic measuring apparatus for measuring the contrast of an imaging system having an optical system and an imaging element that captures an image formed by the optical system,
A test pattern having a predetermined luminance distribution;
Sampling means for sampling an output value when the test pattern output from the image sensor is imaged,
A variance calculating means for calculating a variance indicating the distribution of the output value group sampled,
A spatial frequency characteristic measuring apparatus for an imaging system, comprising: contrast calculation means for calculating the contrast of the imaging system using the calculated dispersion . In a spatial frequency characteristic measuring method for measuring a spatial frequency characteristic of an imaging system having an optical system and an imaging element that captures an image formed by the optical system,
An imaging step of imaging a plurality of test patterns, each having a luminance distribution having a different spatial frequency;
For each test pattern, a sampling step for sampling the output value when the test pattern output from the image sensor is imaged,
A variance calculating step for calculating the variance of the sampled output value group for each test pattern;
A contrast calculation step for calculating the contrast of the imaging system by multiplying the square root of the calculated variance by a constant for each test pattern;
A high-intensity block output measurement step of imaging a high-intensity block pattern having a luminance value equivalent to the maximum luminance value in the test pattern and obtaining an output value of the high-intensity block pattern;
A low-luminance block output measurement step of capturing a low-luminance block pattern having a luminance value equivalent to the minimum luminance value in the test pattern and obtaining an output value of the low-luminance block pattern;
For each test pattern, the normalization for normalizing the contrast calculated in the contrast calculation step using the output value acquired in the high luminance block output measurement step and the output value acquired in the low luminance block output measurement step. Step,
The imaging includes a spatial frequency characteristic calculation step of calculating a spatial frequency characteristic based on the contrast of the imaging system in each test pattern normalized in the normalization step and the spatial frequency of each test pattern System spatial frequency characteristics measurement method.

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