JPH04307347A - Method for evaluating optical converging lens array - Google Patents

Abstract

PURPOSE:To accurately detect the partial falling of the resolving power of a light converging lens array and to faithfully evaluate the optical characteristics or said lens array by calculating the area of an imaginary reference rectangular wave to calculate the area of an actual output waveform and numeralizing the collapse of an image on the basis of the ratio of both areas. CONSTITUTION:The ratios of the areas S1, S2 of an actual output waveform to the areas S3, S4 of an imaginary reference rectangular wave are calculated and, since the actual output waveform is near to a rectangular wave as the ratios become high and near to a triangular wave as said ratios become low, the quality of resolving power can be judged. Further, the output waveform is near to the rectangular wave as the ratio of width ab cutting a reference level to width cd cutting a medium level becomes high and near to the triangular wave as the ratio of said width ab becomes low. Furthermore, since the output waveform is near to the rectangular wave as the differential coefficient of the tangential line an the crossing of the output waveform and the medium level becomes large and near to the triangular wave as said coefficient becomes low, the quality of resolving power can be judged and the optical characteristics of a long light converging lens array can be accurately evaluated over the total length of said lens array and, when a trouble is discovered, the cause thereof can be easily elucidated.

Description

[Detailed description of the invention]

0001

[Industrial Application Field] The present invention uses an output waveform obtained by receiving an image from a light focusing lens array with a rectangular wave grating pattern using a sensor, and digitizes the shape of the waveform to improve resolution. The present invention relates to a method for evaluating optical characteristics of a light-focusing lens array that enables faithful evaluation.

0002

2. Description of the Related Art A light-converging lens array is an optical component in which a large number of fine gradient index rod lenses are arranged to form one continuous image as a whole. The optical characteristics (resolving power) of the light-focusing lens array change due to variations in the characteristics of each rod lens (such as slight differences in refractive index distribution) or disturbances in the arrangement of the rod lenses. MTF (Modulation
Transfer Function). As shown in FIG. 7, this is a square wave grating pattern (original image) 12
The sensor receives an image 16 from the light converging lens array 14, and determines the maximum value imax and minimum value i of the light intensity level.
This is a method of calculating from mim using the following formula. MTF (%) = [(imax − imim ) / (
imax + imim )]×100 and the above MTF
The closer the value is to 100%, the more faithful the image is to the original image (higher resolution).

[0003]Actual measurements are performed using different inspection apparatuses depending on the type of use by the user (line scanning or area scanning), but for example, in the case of line scanning, an optical system as shown in FIG. 8 is used. Light from a halogen lamp 20 passes through a filter 21, a diffuser plate 22, and a square wave test chart 23 to form a square wave grating pattern, which is imaged by a light focusing lens array 12 and received by a CCD image sensor 24. and converts it into an electrical signal. By moving the light converging lens array 12 in the direction of the white arrow, the entire length thereof is inspected. The output waveform is sent to the data processing device 25, and the maximum value ima
Find x and the minimum value imim, and calculate MTF.

0004

[Problems to be Solved by the Invention] However, the MTF value based on the above formula does not necessarily faithfully reflect the resolving power of the light focusing lens array, and even if the MTF value is high, image distortion may occur. When scanning the lens array in the longitudinal direction, defects such as areas where the image shakes may be found.

The reason for this is that when calculating the MTF value, the maximum value imax and the minimum value imim of the output waveform (light level) are
This is because the difference in shape in the output waveform as shown in FIG. 9 cannot be detected because only the difference in shape is taken into account. In FIG. 9, when A and B are compared, in the case of B, the image is distorted. Furthermore, when comparing C and D, there is a phase shift in D, and when the lens array is scanned in the longitudinal direction, the image oscillates. However, since the maximum value and minimum value are the same in both cases, the same MTF value can be obtained regardless of the shape of the output waveform. In other words, resolution cannot be evaluated faithfully using conventional MTF values.

An object of the present invention is to eliminate the above-mentioned drawbacks of the prior art, and to use the conventional optical system for MTF inspection as is, to accurately detect a partial drop in the resolution of a light-focusing lens array. It is an object of the present invention to provide a method that can detect and evaluate optical characteristics more faithfully, and also to provide a method that can elucidate the cause of a drop in resolution.

[0007]

[Means for Solving the Problems] In the present invention, as in the conventional method, first, a sensor receives an image formed by a light-focusing lens array having a rectangular wave grating pattern, and calculates the light intensity level with respect to the position in the longitudinal direction of the lens array. Find the output waveform. Then, the shape of the output waveform (such as whether it is close to a rectangular wave or a triangular wave) is quantified. There are methods shown in A to C in FIG. 1 when converting into numerical values. ■ Find the areas S3 and S4 of the virtual reference rectangular wave determined by the intersection of the output waveform 10 and an arbitrary reference level and the maximum and minimum values of the output waveform, and use the piecewise quadrature method to find the area S1 of the actual output waveform 10. , S2 and find the ratio of both areas (see A in Figure 1). ■ Determine the center level from the maximum and minimum values of the output waveform 10, find the width cd at which the output waveform cuts the center level, and the width ab at which the output waveform cuts the reference level set at an arbitrary amplitude position,
A method to find the ratio of both widths (see B in Figure 1). (2) A method in which the center level is determined by the maximum and minimum values of the output waveform 10, and the differential coefficient of the tangent t at the intersection of the output waveform and the center level is determined (see C in FIG. 1). The above three methods quantify image distortion, and ■
Methods (1) and (2) are simplified versions of methods (2).

In order to quantify the phase shift of the output waveform, the method shown in FIG. 1D is used. ■The center level is determined by the maximum and minimum values of the output waveform 10, and one peak (or trough) is determined from the slope of the tangent of the output waveform at an intermediate level (for example, ±1/2 level) that is a certain amplitude away from the center level. A method of finding the intersection g of both tangent lines that sandwich the , and finding the difference oh between the midpoint coordinate o of the width where the output waveform 10 crosses the intermediate level and the longitudinal direction coordinate h of the lens array of the intersection g. Note that method (1) is preferably carried out in combination with methods (1) to (4) above.

[0009]

[Operation] Calculating the ratio of the areas S1 and S2 of the actual output waveform to the areas S3 and S4 of the virtual reference rectangular wave,
The higher the ratio, the closer the wave is to a rectangular wave, and the lower the ratio, the closer the wave is to a triangular wave. Therefore, it is possible to determine whether the resolution is good or bad based on that ratio. Further, when the ratio of the width cd at which the output waveform cuts the center level to the width ab at which the output waveform cuts the reference level is determined, the higher the ratio, the closer it becomes to a rectangular wave, and the lower the ratio, the closer it approaches to a triangular wave. Similarly, when determining the differential coefficient of the tangent at the intersection of the output waveform and the center level, the larger the differential coefficient, the closer it becomes to a rectangular wave, and the smaller the differential coefficient, the closer it becomes to a triangular wave. Therefore, these values can also be used to determine whether the resolution is good or bad.

[0010] From the slope of the tangents of the output waveform at the intermediate level of the output waveform, find the intersection of both tangents that sandwich one peak or valley, and calculate the difference between the coordinates of the midpoint of the output waveform and the coordinates of the intersection in the longitudinal direction of the lens array. If the difference is small, the peak or valley is symmetrical with respect to the midpoint coordinates (in other words, the phase shift is small), and if the difference is large, the peak or valley is at the midpoint coordinates. It can be seen that there is a large asymmetrical relationship (that is, a large phase shift). Also, depending on the sign of the difference, it can be determined which way the peak or valley is tilted.

These values make it possible to accurately evaluate the optical properties of a long light-focusing lens array over its entire length. Furthermore, if a malfunction is discovered, the cause can be easily investigated.

0012

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 2 is a flowchart showing an embodiment of the method of the present invention. The conventional optical measurement shown in FIG. 8 is performed up to the point where an image from a light-focusing lens array with a rectangular wave grating pattern is received by a sensor and an output waveform representing a light intensity level with respect to a position in the longitudinal direction of the lens array is obtained. This is done by using the system as is. Here, as a light receiving sensor,
CCD with 4096 light receiving elements arranged at 7μm pitch
It uses an image sensor. The output from the CCD image sensor is amplified, sampled and held, and then AD converted to a digital value that can be handled by a computer.

First, all AD-converted output values of the CCD image sensor are input into a computer, and data for each pixel is stored. This operation is usually performed over the entire length of the lens array by moving the lens array relative to the CCD image sensor because the length of the CCD image sensor is short. In this example, since the light receiving elements of the CCD image sensor are arranged at a pitch of 7 μm, the resulting pixel pitch is 7 μm. Then, the average of all output values is taken, and the peaks and valleys of the output waveform are detected. Next, calculate the MTF using adjacent peaks and valleys as a set. Mountain value (maximum light level)
imax and valley value (minimum light level) imim
It is calculated using the same formula as in the prior art.

Next, the center level of adjacent peaks and valleys (average value of peaks and valleys) is set. And as shown in Figure 1A,
The areas S1 and S2 of the portion (shaded portion) surrounded by the output waveform 10 and the center level are calculated. This is calculated from the digitized output waveform data by (output value of each pixel) ×
(pixel pitch) using the piecewise quadrature method. Furthermore, the area S3 of the virtual reference rectangular wave is determined by the intersection of the output waveform 10 and the center level and the maximum and minimum values of the output waveform.
, S4 are calculated. Then, calculate the MTFS value using the following formula. MTFS (%) = [(S1 +S2)/(S3
+S4)]×100 The area of the part surrounded by the output waveform and the center level by this MTFS value (shape of the output waveform)
Evaluate. In this embodiment, the area is calculated above and below the center level, but it does not necessarily have to be at the center level, and may be calculated above and below a certain reference level.

Further, as shown in FIG. 1D, a ±1/2 level is set as the average value between the center level and the peak or valley. And the intersection position e of the ±1/2 level and the output waveform,
Find the slope of the tangent to the output waveform at f. Find the intersection g of the tangent lines that sandwich one mountain (or valley), and find the midpoint o and g of ef.
The distance oh between the foot h of the perpendicular drawn from ef to ef is determined, and the value including its sign is defined as the phase shift. In this example, ±1/2 level is set, but it is not necessarily ±1/2 level.
/2, and an intersection at a preset intermediate level may be used. However, in order to find the intersection of tangent lines, it is preferable not to be too close to the center level or the local maximum/minimum value level. The midpoint may be set at the center of the intersection between the output waveform and the center level.

The calculations for determining MTF, MTFS, and phase shift as described above are performed over the entire length of the light focusing lens array, and the average value, maximum value, and minimum value are calculated for MTF and MTFS, and + for the phase shift. Calculate the average value, maximum value, and deviation value for each side and − side. The shape of the output waveform (whether it is close to a rectangular waveform or triangular waveform) can be evaluated based on the MTFS value, and the variation in the symmetry of each peak/trough in the output waveform can be evaluated based on the phase shift.

Next, the effectiveness of the method of the present invention will be explained based on actual measurement data and theoretical values. A in FIG. 3 shows actual measured values showing changes in the output waveform from the CCD image sensor and MTFS values for each spatial frequency. Also, B is M for typical waveform shapes (square wave, sine wave, triangular wave).
It shows the TFS value. From these facts, it can be seen that the waveform shape can be expressed better by the MTFS value in the present invention.

FIG. 4 shows an example of evaluation based on MTFS values for two light focusing lens arrays with no difference in MTF values. Comparing A and B, A has a well-organized output waveform and good resolution, whereas B has a distorted output waveform with some triangular wave-like parts, and a drop in resolution can be seen. In the conventional evaluation method using MTF, MTF (min) ≒
Although no difference appears at 65%, in the evaluation method using MTFS, a large difference occurs in the case of A with MTFS (min) ≈64% and in the case of B with MTFS (min) ≈48%. This proves that differences in waveform shapes (differences in resolution) can be successfully detected based on the MTFS values according to the present invention.

FIG. 5 shows an example of measurement of phase shift. A is the position (part) in the length direction of the light focusing lens array
The output waveform at is shown. If you look at the shape of the waveform mountain,
It can be seen that symmetrical parts (upright), parts leaning to the left (left leaning), parts leaning to the right (right leaning), etc. are irregularly distributed. B is a graph in which the rightward tilt shift is set as + for the mountain side and the valley side, and the order of mountain → valley → mountain → . . . is plotted on the same graph. Comparing A and B, in A, the output waveform changes from left to right as "upright → left tilt → upright → right tilt → upright", whereas the phase shift is "≒0→≒
-20→≒0→+15→≒0'', which indicates a good correspondence. Therefore, if you look at the graph B, you can clearly see whether the output waveform is tilted to the right or left, and its range and degree.

FIG. 6 shows an example in which MTFS and phase shift are applied to the entire length of a light focusing lens array. A is MT
These are actual measured values of F value, MTFS value, and phase shift. The drop in the MTFS value is noticeable in the part marked with an arrow, and the phase shift is also large, so B shows an enlarged view of the actual output waveform in that part. In fact, it can be seen that the waveform shape is partially close to a triangular wave shape, and that there are leftward and rightward inclinations. Therefore, the method of the present invention can clearly detect a partial drop in resolution, which was difficult to detect with MTF.

The data shown in FIGS. 4 to 6 are examples of measurement at a spatial frequency of 6 lp/mm for a light-focusing lens array with an aperture angle (half angle) of 12 degrees, number of rows of 2, and conjugate length of 32 mm.

[0022]

As described above, since the present invention uses the output waveform shape of the light receiving sensor as an evaluation criterion, it is possible to accurately detect a partial drop in resolution of a light-focusing lens array. A drop in the resolution of the lens array appears as a collapse of the output waveform. Conventional MTFs focus only on maximum and minimum values and cannot detect this collapse of the output waveform, but the present invention evaluates the output waveform shape as it is, so the above effects can be obtained.

Furthermore, in the present invention, since the phase shift of the light-focusing lens array can be detected, the partial drop in resolution of the light-focusing lens array can be caused by: (1) variation in one period length between lens elements, (2) variation in the arrangement of lens elements. It is possible to identify whether this is due to disturbance or disturbance. Even if there is a variation in one period length between lens elements, if the arrangement is perfect, the output waveform will be disturbed but no phase shift will occur. On the other hand, if the arrangement of the lens elements is disordered, a phase shift and a waveform collapse occur. Therefore, by the method of the present invention, the cause of the drop in resolution can be ascertained.

[Brief explanation of drawings]

FIG. 1 is a diagram explaining the principle of the method of the present invention.

FIG. 2 is a flowchart showing one embodiment of the method of the present invention.

FIG. 3 is an explanatory diagram showing that a waveform shape can be expressed by the MTFS value of the present invention.

FIG. 4 is an explanatory diagram showing an application example of MTFS value evaluation of the present invention.

FIG. 5 is an explanatory diagram showing an example of measuring a phase shift according to the present invention.

FIG. 6 is an explanatory diagram showing an example of application of the MTFS and phase shift of the present invention to the entire length of a lens array.

FIG. 7 is an explanatory diagram of MTF values.

FIG. 8 is an explanatory diagram of an optical system for evaluating optical characteristics.

FIG. 9 is an explanatory diagram showing the relationship between output waveforms, image collapse, and phase shift.

[Explanation of symbols]

10 Output waveform 12 Square wave grid pattern 14 Light focusing lens array 16 Image 20 Halogen lamp 21 Filter 22 Diffusion plate 23 Square wave test chart 24 CCD image sensor 25 Data processing device

Claims (4)

[Claims] 1. A sensor receives an image formed by a light-converging lens array having a rectangular wave grating pattern, obtains an output waveform representing a light intensity level with respect to a position in the longitudinal direction of the lens array, and compares the output waveform with an arbitrary reference level. Find the area of the virtual reference rectangular wave determined by the intersection point and the maximum and minimum values of the output waveform, calculate the area of the actual output waveform using the piecewise quadrature method, and quantify the distortion of the image by the ratio of both areas. A method for evaluating optical characteristics of a light-focusing lens array. 2. An image formed by a light-converging lens array having a rectangular wave grating pattern is received by a sensor, an output waveform representing a light intensity level with respect to a position in the longitudinal direction of the lens array is obtained, and the maximum value and minimum value are used to determine the center A light source characterized by determining the level, determining the width at which the output waveform cuts the center level, and the width at which the output waveform cuts the reference level set at an arbitrary amplitude position, and quantifying the image distortion based on the ratio of both widths. Method for evaluating optical properties of focusing lens arrays. 3. A sensor receives an image formed by a light-converging lens array having a rectangular wave grating pattern, obtains an output waveform representing the light intensity level with respect to a position in the longitudinal direction of the lens array, and determines the center by the maximum value and minimum value of the output waveform. A method for evaluating optical characteristics of a light-focusing lens array, characterized by determining a level and quantifying image distortion by a differential coefficient at the intersection of an output waveform and a center level. 4. An image formed by a light-converging lens array having a rectangular wave lattice pattern is received by a sensor, an output waveform representing a light intensity level with respect to a position in the longitudinal direction of the lens array is obtained, and the maximum value and minimum value are used to determine the center Determine the level, find the intersection point of both tangent lines from the slope of the tangent line of the output waveform at an intermediate level separated by an arbitrary amplitude from the center level, and calculate the difference between the midpoint coordinate of the output waveform and the longitudinal direction coordinate of the lens array of the intersection point. A method for evaluating optical characteristics of a light-focusing lens array, characterized in that the difference is calculated as a phase shift at that position.