JPH037799Y2 - - Google Patents

Description

[Detailed Description of the Invention] (Technical Field) This invention relates to a device for measuring the resolution of a lens.

(Prior Art) A resolution measurement method is known in which the resolution of a lens is measured and evaluated using a spatial frequency chart and a solid-state image sensor.

FIG. 1 conceptually shows an apparatus using such a measurement method. Symbol R represents a lamp, symbol C represents a spatial frequency chart, symbol L represents a lens to be tested, and symbol I represents a solid-state image sensor.

The spatial frequency chart C is as shown in FIG.
Although it has a black and white striation group pattern formed at regular intervals, it may have a pattern in which the density spatially changes sinusoidally at a constant period instead of such a striation group pattern.

As shown in FIG. 2, the solid-state image sensing device has a light receiving section 100 and a terminal 101, and in this light receiving section 100, minute photo elements are arranged in a row at a minute pitch. Such a solid-state image sensor has a self-scanning function. Examples of solid-state image sensors include CCDs, BBDs, PDAs, and the like.

Now, to measure the resolution of the lens L to be tested,
Do as follows. That is, using a spatial frequency chart C having a spatial frequency pattern to be measured, illuminating this spatial frequency chart C with a lamp R, and measuring the spatial frequency chart C by the lens L to be measured.
An image Im is formed on the light receiving part of the solid-state image sensor I,
This image Im is scanned by the solid-state image element I, and a predetermined calculation is performed on the output of the element I to calculate the MTF, and the resolution with respect to the above-mentioned spatial frequency is evaluated based on this MTF.

In this way, by using the solid-state image sensor and the spatial frequency chart, it is possible to automatically and quickly measure and evaluate the resolution of the test lens for the spatial frequency to be measured.

However, such a resolution measurement method has a problem in that the measured value fluctuates significantly.

This variation in measured values is due to the structure of the solid-state image sensor.

For example, if the photo element's aperture width is
Using Fairchild's CCD with an array pitch of 0.008mm and 0.013mm as a solid-state image sensor,
Assuming that the resolution is measured, the obtained
If we theoretically calculate the MTF variation region and display the spatial frequency as a variable, we get something like the one shown in Figure 3.

The horizontal axis is the spatial frequency (unit: C/mm), and the vertical axis is the spatial frequency (unit: C/mm).
Indicates MTF. The MTF in Figure 4 is calculated theoretically under certain conditions for the above CCD.
It is your own MTF, called Aperture Your Sampling Response, and is denoted as ASR.

In Figure 3, the symbol ASRMX is the maximum value of ASR,
The symbol ASRMN is a curve indicating the variation of the minimum value of ASR, and ASR varies between the maximum value and the minimum value according to each spatial frequency.

Figure 4 shows the magnitude of ASR variation at each spatial frequency. The solid-state image sensor itself
Since the MTF fluctuates as described above, the measured resolution of the lens under test will also fluctuate under the influence of the ASR fluctuation.

(Purpose) The purpose of the present invention is to provide a device for measuring the resolution of a lens using a spatial frequency chart and a solid-state image sensor, which measures the resolution as accurately as possible.
The goal is to provide equipment that can be evaluated.

(composition) The present invention will be explained below.

The device of the present invention includes a spatial frequency chart, illumination means, holding means, and a solid-state image sensor.

The spatial frequency chart has a pattern of black and white striations formed at regular intervals, or a pattern in which the density changes spatially at a constant period in a sinusoidal manner.

The holding means holds the lens to be tested.

The illumination means illuminates the spatial frequency chart.
Note that the spatial frequency chart may be translucent or reflective. As the holding means and illumination means, conventionally known ones may be used as appropriate.

An image of the spatial frequency chart by the test lens is formed on the light receiving section of the solid-state image sensor. Let m be the magnification of this image.

The solid-state image sensor scans the image, and the MTF is calculated according to its output, thereby evaluating the resolution of the lens to be tested.

Now, the features of the present invention are as follows. That is, the spatial period X _T of the spatial frequency chart and the photo element pitch X _O of the solid-state image sensor are determined so that X _T = (2M+1)/mX _O (1) for a natural number M and a magnification m. . Conventional lighting means, holding means, etc. may be used as appropriate.

Incidentally, lenses generally have a fixed purpose from the time they are manufactured.
For example, if we consider a copying machine lens, it is generally used at the same magnification.
The required resolution is also about 5C to 10C/mm. Therefore, in order to evaluate the resolution of such a lens, it is sufficient to know the resolution near the above-mentioned spatial frequency when the lens is used at the same magnification. for example
When measuring a spatial frequency resolution of 6C/mm,
It doesn't have to be exactly 6C/mm, it just needs to be around 6C/mm, and the performance of the lens can be sufficiently evaluated even if it's 5.9C/mm or 6.1C/mm.

On the other hand, since the measuring device uses a solid-state image sensor, the resolution of the lens to be tested inevitably changes due to fluctuations in the ASR of the solid-state image sensor.

Therefore, in order to perform accurate resolution measurement, it is necessary to perform this under conditions where the fluctuation of the ASR is small. Referring now to FIG. 4, this condition is best at the minimum value of the curve in FIG. The condition (1) above provides the best conditions.

Let me explain this below.

In FIG. 5, the symbol P indicates a photo element of a solid-state image sensor. The code i indicates that the photo element P is the i-th photo element counted from the reference photo element. Further, X _O represents the photo element pitch, and X ₁ represents the aperture width of the photo element P.

Now, suppose that a light intensity distribution is given in which the intensity F _(X) is given by F _(X) = 1/2 {1 + cos (2πux + θ)} (2) in the direction in which such photo elements are arranged. For example, it is sufficient to imagine a state in which an ideal equal-magnification image of a spatial frequency chart having a pattern in which density changes sinusoidally at spatial frequency u is formed on the photoelement array surface.

At this time, consider the photoelectric conversion output Von at the n-th photo element P counting from the reference photo element. Please refer to FIG. Considering that the photo element pitch is X _O , it will be easily understood that the distance from the reference position to the center of the nth photo element is X _O n.

In addition, the photoelectric conversion characteristics of each photo element
S _(X ′ ₎ , Then, as is clear from Figure 6,
Von is given as follows.

=(1/2)[1+cos{(u/u ₀ )2πn+θ} ·sin(πuX ₁ )/πuX ₁ ]X ₁ (4) However, here, X _O is set to 1/u ₀ . u ₀ is
is the spatial frequency of the photoelement array.

In this equation (4), if n that gives the maximum and minimum of Von within one period of spatial period 1/u are n' and n'', respectively, then ASR is ASR=Von'-Von''/{ It is given by Von}max+{Von}mix(5). {Von}max and {Von}min represent the maximum value and minimum value of Von, respectively.

{Von}max is the value of Von when u and θ become 0 in the limit, that is, when u→0, θ→0, and this is the sinusoidal light intensity given by equation (2) This occurs when the spatial period of the distribution is extremely long. Also, {Von}min is defined when u becomes 0 in the limit and the spatial phase shifts by π, that is, u→0, θ
→This is the value of Von when π.

Considering this, from equation (4), ASR=1/2sin(πux ₁ )/πux ₁ {cos (u/u ₀ 2πn′+θ)−cos(u/u ₀ 2πn″+θ)
}(6) is obtained.

Here, if n'=0 with the n'th photo element as the reference, then from equation (6), ASR=sinπux ₁ /πux ₁ sin(u/u ₀ n″π+θ) ・sin(u/u ₀ n″π) (7) is obtained.

From this, the MTF of the solid-state image sensor is
It can be seen that ASR varies with photoelement pitch X _O =1/u ₀ , aperture width X ₁ , and phase θ. Among these, X _O and X ₁ are constants specific to the solid-state image sensor, so in the end, the spatial frequency u
The ASR for θ changes depending on θ.

Therefore, next, as the relationship between the spatial frequency u and the spatial frequency u ₀ =1/X _O of the photoelement array, we have the following two relationships: (i) u=u ₀ /2M, (ii) u=u ₀ /2M+1 Let's consider the case. Note that here, M is a natural number 1, 2, 3, . . . . First, looking at case (i), considering that n″=M=u ₀ /2u, equation (7) is transformed into ASR=sinπux ₁ /πux ₁ cosθ (8).

In FIG. 7, the solid line sine curve is F(θ=
0) is shown. The number written below the photo element P is not a code, but indicates the rank of the corresponding photo element from the reference position. The position of the reference photo element, which is the 0th photo element, coincides with the position of the maximum value of the light intensity distribution F (θ=0). Further, the position of the maximum value to the right of this maximum value coincides with the position of the 2Mth photo element.

In Figure 7, the sine curve indicated by the broken line is F(θ=θ)
The case is shown below. As can be seen from this, θ is the phase shift with respect to the sine curve F (θ = 0) that should be the reference, in other words, the solid-state image sensor and the image of the spatial frequency chart formed on its light receiving part. It represents the parameter corresponding to the relative deviation of . This phase shift causes the ASR shift,
In other words, it appears as fluctuations.

When measuring resolution, variation in θ is unavoidable, and due to this variation in θ, the measured resolution will vary even if the resolution of each tested lens is exactly the same. . The reason for this is that the solid-state image sensor
The reason lies in the dependence of ASR on θ.

Now, under the condition of u < (u ₀ /2), if we find the maximum and minimum values of ASR given by equation (8), we get the maximum value (ASR) max and the minimum value (ASR) min. are, respectively, and ASR is in this case (ASR)max~
(ASR) will fluctuate in the min area.

Next, looking at case (ii) above, in this case, n″=M=u ₀ /2u−1/2, so from equation (7), ASR is: ASR={(sinπuX ₁ ) /πuX ₁ }cos(u/2u ₀ )π−
θ} cos {(u/2u ₀ )π} (10) is given.

In FIG. 8, the solid line sine curve shows the case of F (θ=0), and the broken line shows the case of F (θ=θ). F (θ=0)
In the case of , the position of the maximum value is 0th and 2M+
This matches the position of the first photo sensor.

Under the condition that u < (u ₀ /2), the maximum and minimum values of ASR (ASR)'max and (ASR)'min given by equation (10) are θ
occurs when u/2u ₀ π and 0, respectively. is given. Therefore, the range of ASR variation at this time is from (ASR)'max to (ASR)'min.

Now, let's take again the Fairchild CCD that I mentioned earlier as an example. In this CCD, X ₁ =0.008 mm and X ₀ =0.013 mm.

Substitute these values into each of (9) and (11),
(ASR)max−(ASR)min, (ASR)′max−
(ASR)′min is calculated, and when conditions (i) and (ii) are considered, (ASR)max−(ASR)min corresponds to the maximum value of the curve in Figure 4, and ( ASR)′max
It can be seen that -(ASR)'min corresponds to the minimum value of the curve in FIG.

That is, if condition (ii) above is selected,
Under this condition, fluctuations in the ASR of the solid-state image sensor,
That is, the range of ASR variation due to variation in position θ becomes minimal. Therefore, under this condition, resolution measurements as accurate as possible are possible.

Considering that u=1/X _T (X _T is the spatial period of the spatial frequency chart) u ₀ =1/X _O , condition (ii) is equivalent to X _T = (2M+1)/1X _O. be. Therefore, if we consider the magnification m of the chart image formed by the test lens on the light receiving part of the solid-state image sensor, when the condition X _T = (2M + 1)/mX _O is selected, The resolution of the lens to be tested can be measured and evaluated in a state with the least amount of variation, that is, in a state where the distribution area of variation is the smallest. In the above explanation, the spatial frequency chart in which the density changes sinusoidally is taken as an example, but it goes without saying that the spatial period X _T in the chart of black and white lines is determined as shown in FIG.

(Effects) As described above, according to the present invention, it is possible to provide an apparatus for measuring the resolution of a lens, which can perform measurement while minimizing the variation in the measured value of the resolution.

[Brief explanation of the drawing]

Figures 1 and 2 are diagrams for explaining the prior art, Figures 3 to 8 are diagrams for explaining the principle and effects of the present invention, and Figure 9 is a diagram for explaining the prior art.
FIG. 3 is a diagram for explaining the spatial period of a spatial frequency chart formed by a group of black and white lines. R...Lamp (illumination means), C...Spatial frequency chart, L...Test lens, I...Solid-state image sensor, P...Photo element.

Claims (1)

[Claims for Utility Model Registration] A group of black and white lines formed at regular intervals or a spatial frequency chart whose density changes spatially in a sinusoidal manner at a constant period, and an illumination means for illuminating this frequency chart. , a holding means for holding a test lens whose resolution is to be measured, and a solid-state image sensor, which forms and projects an m-magnification image of the spatial frequency chart onto the solid-state image sensor using the test lens; This is a device that evaluates the resolution of a test lens based on the output of a solid-state image sensor, where X _T is the spatial period of the spatial frequency chart, and X _O is the photoelement pitch of the solid-state image sensor, and these X _T , A device for measuring the resolution of a lens, characterized in that X _O is determined to satisfy the relationship: X _T =(2M+1)/mX _O for a natural number M and the above-mentioned magnification m.