JPH09105705A - Analyzing method and analyzer for micro lens aggregate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily analyze intensity distribution, resolution, light quantity unevenness, resolution unevenness of a point image of a micro lens aggregate by using intensity distribution of a point image of each micro lens and constituting an analyzing method and analyzer to obtain the intensity distribution and the resolution of the point image of the micro lens aggregate. SOLUTION: It is determined whether a single lens constituting a lens array is in a light receiving area toward a light source or not, and if it is in the light receiving area, analysis is carried out and a wave front aberration is calculated. After a coordinate transformation, in which the calculated wave front aberration of the single lens is rotated in the center direction of the single lens to an optical axis of the lens array, is carried out, a pupil function including the wave front aberration is transformed on the basis of the Fourier transformation, and then, an intensity distribution of the point image of the single lens is obtained. All the obtained intensity distributions of the point images of all the single lenses are added together, and the intensity distribution of the point image of the lens array is obtained. Subsequently, an absolute value of the obtained intensity distribution of the point image of the lens array is squared so as to be transformed on the basis of the Fourier transformation, and the resolution MTF of the lens array is calculated.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an analysis method and an analysis apparatus for a microlens assembly, and more particularly to an analysis method and an analysis apparatus for analyzing a point image intensity distribution and resolution of a microlens assembly.

[0002]

2. Description of the Related Art Conventionally, as a method of analyzing the intensity distribution and resolution of a point image of a single lens, a ray tracing method for sequentially calculating the situation in which one ray passes through each surface of an optical system, or a three-dimensional Aberration analysis methods and the like are known.

However, in the fields of optical communication, image processing, optical information processing, etc., so-called microlenses have become important as optical component elements, and moreover, they are composed of a plurality of microlenses rather than a single lens. Microlens assemblies have come to be used.

For example, in the field of image processing such as an image forming optical system of a copying machine, a reading unit of a facsimile, an optical system of a printer, optical communication, optical information processing and the like, a large number of refractive index distribution type lenses, which are minute lenses, are used. By using a lens array, which is an array of minute lenses that are arranged so as to form one continuous image as a whole, a uniform image can be obtained without a decrease in light amount and resolution, and the optical system can be downsized. It is known to be able to.

In addition, recently, a microlens assembly having a higher resolution and a bright characteristic, such as a lens array used as a relay lens for a high resolution printer or a liquid crystal light valve, is required. Therefore, it is becoming important to analyze the intensity distribution and resolution of the point image of the microlens assembly in order to obtain the microlens assembly having the required characteristics.

[0006]

However, in the ray tracing method and the three-dimensional aberration analysis method for analyzing the intensity distribution and resolution of the point image of the single lens described above, the microlens assembly is composed of a plurality of microlens assemblies. Because it is an assembly of minute lenses,
It is not possible to analyze the intensity distribution and the resolution of the point image by viewing the minute lens aggregate as one lens.

Further, since the image formed by the microlens assembly is formed by overlapping the images formed by the individual microlenses, light amount unevenness and resolution unevenness occur on the image surface. However, such light amount unevenness and resolution on the image surface occur. The unevenness is an important index of the microlens assembly. However, it is not possible to analyze such light amount unevenness and resolution unevenness of the minute lens aggregate by the ray tracing method and the three-dimensional aberration analysis method for analyzing the intensity distribution and resolution of the point image of the single lens in the related art.

The present invention has been made in view of the above points, and it is possible to easily analyze the intensity distribution and resolution of a point image of a microlens assembly and easily analyze unevenness of light amount and unevenness of resolution. An object of the present invention is to provide an analysis method and an analysis device for a microlens assembly.

[0009]

In order to solve the above problems, a method of analyzing a microlens assembly according to claim 1 analyzes the intensity distribution and / or the resolution of a point image of a microlens assembly including a plurality of microlenses. In the analysis method, the exit pupil including the wavefront aberration of each microlens is calculated, and the exit pupil including the calculated wavefront aberration of each microlens is directed toward the center of the microlens with respect to the optical axis of the microlens assembly. After rotation, we obtain the point image intensity distribution of each microlens,
The intensity distribution and / or resolution of the point image of the microlens assembly is obtained by using the intensity distribution of the point image of each individual microlens.

According to a second aspect of the present invention, there is provided an analyzing device for analyzing the intensity distribution and resolution of a point image of a microlens assembly composed of a plurality of microlenses. A means for calculating the coordinate of the calculated wavefront aberration into a wavefront aberration for the optical axis of the microlens assembly, and Fourier transform of the wavefront aberration of each microlens subjected to coordinate conversion to obtain the point of each microlens. A means for obtaining the intensity distribution of the image, a means for obtaining the intensity distribution of the point image of the minute lens aggregate by adding the intensity distribution of the point images of the individual minute lenses, and a means for obtaining the intensity distribution of the point image of the minute lens aggregate. The absolute value is squared and Fourier transformed to obtain the resolution of the microlens assembly.

[0011]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the accompanying drawings. First, an example of a microlens assembly that is analyzed by the method and apparatus for analyzing a microlens assembly according to the present invention will be described with reference to FIGS. 1 and 2. Note that FIG. 1 is a schematic view of an external main part showing an example of a lens array that is a microlens assembly, and FIG. 2 is a main part schematic view of the lens array of FIG.

This lens array 1 comprises a rod-shaped radial gradient index rod lens 2 which is a large number of minute lenses.
It is a stack of bales. The radial direction gradient index rod lens 2 is formed by subjecting a rod-shaped multi-component glass to ion exchange to provide a parabolic gradient index distribution in the radial direction.

Here, the number of radial direction gradient index rod lenses 2 of the lens array 1 is set to 50, and the light receiving area for the light source 5 on the optical axis 3 is set to the range indicated by the light receiving area 4. 1 and 2, only 12 lenses out of 50 radial direction gradient index rod lenses 2 (which will be referred to as "lenses L1 to L12") are illustrated in FIGS. Shows.

Therefore, the analysis processing by the analysis apparatus for the microlens assembly according to the present invention will be described with reference to FIG. The analysis device that executes this analysis process can be configured by a known computer.

In this analysis processing, first, after inputting the lens parameters and the calculation range, the number of individual microlenses (hereinafter referred to as "single lens") forming the lens array is input, and then the analysis is performed. Start. And
It is determined whether or not the single lens forming the lens array is in the light receiving region with respect to the light source, that is, whether or not the single lens is a target (analysis target) for calculating the intensity distribution of the point image. If the single lens is not in the light receiving area, the lens to be analyzed is changed to the next single lens.

If the single lens is in the light receiving region, that is, if it is a single lens to be analyzed, the single lens is analyzed by the known three-dimensional aberration analysis method or ray tracing method to obtain the wavefront aberration ( OPD: Optical
Path Diffraction). In this case, since the center of the single lens does not coincide with the optical axis of the lens array, coordinate conversion was performed to rotate the calculated wavefront aberration of the single lens in the direction of the center of the single lens with respect to the optical axis of the lens array. After that, the pupil function including the wavefront aberration (Pupil F
Fourier transform of the unction) to obtain the intensity distribution (PSF: Point) of the point image of the single lens viewed from the optical axis of the lens array.
Spread Spread). Then, the intensity distribution of the obtained point image of the single lens is added to the intensity distribution of the already obtained point image of the single lens to obtain the intensity distribution of the point image of the lens array.

After that, whether or not the point image intensity distributions have been obtained for all the single lenses constituting the lens array,
That is, it is determined whether or not the number of input lenses has been reached, and the above-described processing is repeatedly executed until the number of input lenses is reached.

When the number of input lenses is reached, that is, the point array of the lens array, which is the result of adding up the intensity distributions of point images for all the single lenses in the light receiving region, forming the lens array. When the intensity distribution is obtained, the absolute value of the obtained intensity distribution of the point image of the lens array is squared and Fourier transformed to obtain the resolution MT of the lens array.
Calculate F.

In this way, when the intensity distribution of the point image of the lens array and the resolution MTF for the input lens parameters are obtained, it is determined whether or not the lens parameters are within the calculation range, and the lens parameters are calculated. If it is within the calculation range, the input parameter value is changed, and the above-described processing is repeatedly executed for the changed lens parameter, so that the intensity distribution of the point image of the lens array and the resolution MTF (Modulat) for each lens parameter are changed.
Ion Transfer Function).

A case in which this analysis processing is applied to the lens array 1 of FIG. 1 to perform analysis will be specifically described. First, it is assumed that the lens array 1 has the parameters shown in Table 1 and has the radial direction refractive index distribution represented by the equation (1).

[0021]

[Table 1]

[0022]

(Equation 1)

Therefore, as shown in FIG. 2, the lens array 1
As described above, the light receiving range of each of the radial direction gradient index rod lenses 2 with respect to the light source on the optical axis 3 of
And At this time, the direction of the center 6 of each of the radial direction gradient index rod lenses 2 viewed from the optical axis 3 of the lens array 1 is as shown by an arrow 7.

Here, for example, among the 50 individual radial direction gradient index rod lenses 2 constituting the lens array 1, the 12 shown in FIGS. 1 and 2 will be analyzed. In performing the process, the initial value of the fourth-order coefficient h ₄ of the refractive index (here, from Table 1 to “−1.0”) and the calculation range (also from Table 1 to “−1.0 to 2.0”) are used as lens parameters. )). Then, "12" of the lenses L1 to L12 are input as the number of lenses.

In this case, the reason why the fourth-order refractive index h ₄ is used as the lens parameter is as follows. That is, when trying to obtain a desired lens array characteristic, other lens parameters, for example, n ₀ and g are determined to some extent due to the material relationship. The fourth-order coefficient h _{4 of the} refractive index is the only parameter that can be used to adjust the lens performance when manufacturing the lens. The fourth-order coefficient h ₄ of the refractive index is one of the important parameters that determine the lens performance, and by optimizing this coefficient, a lens array with small aberration and high resolution can be obtained.

When the analysis is started, first the lens L
It is determined whether 1 is in the light receiving area 4. As for this determination method, if the determination is made by whether the center of each lens is within the light-receiving region 4, the center of the lens L1 is not within the light-receiving region 4, so the analysis of the lens L1 is performed. Without performing, the lens is changed to the lens L2, and it is similarly determined whether or not it is in the light receiving area 4.

At this time, since the center of the lens L2 is within the light receiving region 4, the lens L2 is used as the lens to be analyzed and analyzed by the three-dimensional aberration analysis method or the ray tracing method to calculate the wavefront aberration of the lens L2. . Then, the obtained wavefront aberration of the lens L2 is subjected to coordinate conversion for rotating the exit pupil in the direction of the center of the lens L2 with respect to the optical axis of the lens array 1, and the pupil function including the wavefront aberration after the coordinate conversion is Fourier-transformed. As a result, the intensity distribution of the point image of the lens L2 is obtained. Then, the intensity distribution of the point image of the lens L2 is added as the intensity distribution of the point image of the lens array 1 (in this case, since the lens L2 is the first lens to be analyzed, the intensity distribution of the point image of the lens L2 is added. Is the intensity distribution of the point image of the lens array 1 as it is.)

Next, when it is judged whether or not the processing for the number of lenses has been completed, since it is not completed, the next lens L
It is discriminated whether or not 3 is within the light receiving area 4, and this lens L3
Since the center of is also within the light receiving region, the lens L3 is analyzed by the three-dimensional aberration analysis method or the ray tracing method in the same manner as described above to calculate the wavefront aberration of the lens L3. Then, the obtained wavefront aberration of the lens L3 is subjected to coordinate transformation and then Fourier transformation to obtain the intensity distribution of the point image of the lens L3.

At this time, the intensity distribution of the point image of the lens L2 obtained previously is obtained by performing the Fourier transform after once converting the wavefront aberration of the lens L2 into the coordinates of the lens array 1, and similarly the point image of the lens L3. The intensity distribution of is also obtained by performing a Fourier transform after once converting the wavefront aberration of the lens L3 into the coordinates of the lens array 1. Therefore, since the point image intensity distribution of the lens L2 and the point image intensity distribution of the lens L3 have the same coordinate system, the point image intensity distribution of the two lenses L2 and the point image intensity distribution of the lens L3 can be simplified. Can be added. Therefore, the intensity distribution of the point image of the lens L3 is added to the intensity distribution of the point image of the previous lens L2 to obtain the intensity distribution of the point image of the lens array 1.

Similarly, since the lens L4 is located outside the light receiving region 4, no analysis is performed and the lenses L5, L6 and L7 are similarly analyzed.
For the lens L, the intensity distribution of the point image is obtained and sequentially added.
No analysis is performed for 8 and L9, point image intensity distributions are obtained for lenses L10 and L11, and they are sequentially added, and analysis is not performed for lens L12. Thereby, the light receiving area 4
The intensity distribution of the point images of the lens array 1 can be obtained by simply adding the intensity distributions of the individual point images of the lenses L2, L3, L5 to L7, L10, and L11.

After the processing for the number of lenses input in this way is completed, the absolute value of the intensity distribution of the point image of the lens array 1 obtained is squared and Fourier transformed to obtain the resolution of the lens array 1. Get MTF.

By performing the above processing, for example, when the lens L3 is analyzed by the three-dimensional aberration analysis method or the ray tracing method to calculate the wavefront aberration OPD, the wavefront aberration in the exit pupil is as shown in FIG. Become. Therefore, by converting the coordinates into the coordinates of the lens array 1, that is, by rotating the exit pupil, the wavefront aberration as shown in FIG. 5 can be obtained.

Therefore, the lenses L2, L in the light receiving area 4
For 3, L5 to L7, L10, and L11, when the exit pupil including the wavefront aberration is rotated, and each is Fourier-transformed and then superposed, the intensity distribution of the point image of the lens array 1 is obtained as shown in FIG. . Further, by performing a Fourier transform on the square of the absolute value of the intensity distribution of the point image of the lens array 1, as shown in FIG.
F is obtained.

When the intensity distribution and resolution of the point image of the lens array 1 for the lens parameters input as described above are obtained, it is determined whether the parameters are within the calculation range. Here, for example, by changing the initial value of the refractive index fourth order coefficient h ₄ from (-1.0) and was analyzed, then the refractive index fourth order coefficient h ₄ to "-0.8", the above-described Similarly, the point image intensity distribution and resolution of the lens array 1 are obtained. Even after that, the fourth-order coefficient h4 is set to "0.2".
The intensity distribution and resolution of the point image of the lens array 1 at each parameter value are obtained until the value is changed to "2.0" in increments, and if the parameter is out of the calculation range, the analysis ends.

As described above, the fourth-order coefficient h ₄ of the refractive index “−”
From the intensity distribution and resolution of the point image of the lens array 1 obtained within the range of 1.0 to 2.0 ”, for example, the spatial frequency 30
The resolution MTF for Lp / mm is obtained as shown in FIG. It can be seen from FIG. 8 that the lens array 1 to be analyzed exhibits the highest resolution MTF when the fourth-order refractive index h ₄ is 0.64 with respect to the spatial frequency of 30 Lp / mm.

As described above, by rotating and analyzing the exit pupils of the individual microlenses including the wavefront aberration toward the center of each lens with respect to the optical axis of the microlens assembly, the intensity of the point image of the microlens assembly is analyzed. Distribution and resolution can be easily analyzed.

That is, when the radial direction gradient index rod lens as a single lens is analyzed, the central axis of the lens is set to the optical axis (Z axis) and the meridian plane is set to Y as shown in FIG.
The −Z plane and the spherical surface are defined as the XZ plane. Then,
As shown in 0, the object A in the normal object plane (the XY plane in which the object A exists) and its image A ′ are meridian planes (YZ
Exist in the plane). Here, when the spot shape of the single lens is calculated, it can be obtained by expanding the pupil function on the mesh and performing Fourier transform. FIG.
Shows an example in which the pupil function of a single lens is expanded on a mesh.

However, when the spot shape of the lens array is calculated, even if the above-described single lens analysis is applied as it is, the arrangement of the object point (light source) and each single lens is as shown in FIG. Since the x and y directions are different from each other, the mesh directions are different as shown in FIG. 13, and the spots calculated from the pupil function of each single lens cannot be superposed. The shape cannot be calculated.

On the other hand, when the pupil function is expanded on the mesh as in the present invention, the coordinates of the function are converted in advance so that the direction of the mesh is not the meridional surface of each lens but the meridional surface of the lens array. By matching, the mesh of each lens can be simply added, the shape of the spot can be calculated, and the resolution of the lens array can be calculated using this. .

Further, since the image formed by the lens array is a superposition of the images formed by the respective lenses, the amount of transmitted light on the image plane is also the sum of the amounts of light of the respective lenses, and uneven light amount and uneven resolution due to the arrangement pitch of the respective lenses occur. When the lens array is viewed as a single lens, unevenness in light quantity and unevenness in resolution are important indices for evaluating lens performance.

Regarding the uneven light quantity and uneven resolution of this lens array, in the above-described analysis processing, the pupil function including the wavefront aberration of the single lens is coordinate-converted in the direction of the center of the single lens with respect to the optical axis of the lens array. The pupil function including the wavefront aberration of each single lens can be simply added by adjusting to the coordinates of, so that it can be easily obtained by calculating the light quantity distribution on the image plane by the unit object (light source) mesh. become able to.

For the minimum unit in the lens array (for example, the lenses L3, L6, and L7 in FIG. 1), when the light quantity distribution on the image plane by the unit object (light source) mesh is obtained, for example, the light quantity distribution as shown in FIG. 14 is obtained. Therefore, the unevenness of the light amount can be known. In addition, light amount unevenness = (PSFmax
-PSFmin) / PSFmax x 100 (%).
Similarly, with respect to the resolution, for example, a resolution distribution as shown in FIG. 15 is obtained, and the unevenness in resolution can be known. In addition, resolution unevenness = MTFmax−MTFmin
(%) Is defined.

Further, unevenness in light quantity and unevenness in resolution are determined for each degree of overlap m of the lens array (the degree of overlap m is defined by the field diameter of the image formed by the lens with respect to the diameter of the radial direction index rod lens element). By obtaining, for example, FIG.
It is possible to obtain an overlapping degree m-light amount unevenness diagram as shown in FIG. 6 and an overlapping degree m-resolution unevenness diagram as shown in FIG.

Here, the degree of overlap m controls light amount unevenness (brightness unevenness) and resolution. If the degree of overlap m is small, the uneven brightness is large and the resolution is high. Therefore, by obtaining the overlapping degree m-light amount unevenness diagram and the overlapping degree m-resolution unevenness diagram as described above, the brightness unevenness is small and the resolution is high, that is, the brightness unevenness is required without correction. It becomes easy to find the degree of overlap m at which the two can be balanced so that the resolution can be obtained.

In the above embodiment, the case where the analysis method and the analysis apparatus according to the present invention analyze the lens array composed of the radial direction gradient index rod lens as shown in FIG. 1 has been described. Not limited to this, for example, the intensity distribution and the resolution of the point image of the minute lens aggregate 11 including the biconvex rod lens 12 as shown in FIG. 18 or the minute lens aggregate 21 including the plano-convex lens 22 as shown in FIG. Analysis can also be performed.

[0046]

As described above, according to the method of analyzing a microlens assembly of claim 1 and the analyzer of the microlens assembly of claim 2, the wavefront aberration of each microlens is calculated. Since the exit pupil including the wavefront aberration is rotated toward the center of the microlens with respect to the optical axis of the microlens assembly, the intensity distribution of the point images of the individual microlenses is added to the microlens assembly. Since the intensity distribution of the point image can be obtained and the resolution can be obtained from this intensity distribution of the point image, the intensity distribution and resolution of the point image of the microlens assembly can be easily analyzed and the lens performance of the microlens assembly can be obtained. It is possible to easily analyze light amount unevenness and resolution unevenness, which are important indices for evaluating the.

[Brief description of the drawings]

FIG. 1 is a schematic view of an external main part showing an example of a lens array that is a microlens assembly.

FIG. 2 is a schematic view of a main part of the lens array of FIG. 1 viewed from an incident side.

FIG. 3 is a flowchart showing an example of analysis processing in which the analysis method according to the present invention is performed.

FIG. 4 is an explanatory diagram showing an example of a wavefront aberration of a minute lens before coordinate conversion obtained by the analysis processing.

FIG. 5 is an explanatory diagram showing an example of wavefront aberration when the wavefront aberration of FIG. 4 is coordinate-converted.

FIG. 6 is an explanatory diagram showing an example of the intensity distribution of a point image of a microlens assembly obtained by the analysis processing.

FIG. 7 is an explanatory diagram showing an example of a resolution MTF of a microlens assembly obtained by the analysis processing.

FIG. 8 is a diagram showing an example of fourth-order refractive index-resolution of a microlens assembly obtained by the same analysis process.

FIG. 9 is an explanatory diagram illustrating a coordinate system of a minute lens (single lens).

FIG. 10 is an explanatory diagram for explaining calculation of a spot shape of a minute lens.

FIG. 11 is an explanatory diagram showing an example of a pupil function of a minute lens.

FIG. 12 is an explanatory diagram for explaining the relationship of the arrangement of each microlens with respect to the light source of the microlens assembly.

FIG. 13 is an explanatory diagram for explaining the arrangement of each minute lens of the minute lens aggregate and the mesh in which the pupil function is expanded.

FIG. 14 is an explanatory diagram for explaining a light amount distribution of a microlens assembly obtained by performing the analysis process.

FIG. 15 is an explanatory diagram for explaining the resolution distribution of the minute lens aggregate obtained by performing the same analysis process.

FIG. 16 is a diagram showing an example of light amount unevenness with respect to the degree of overlap of the microlens assembly obtained by performing the same analysis process.

FIG. 17 is a diagram showing an example of resolution unevenness with respect to the degree of overlap of minute lens aggregates obtained by performing the same analysis process.

FIG. 18 is a schematic view of an external main part showing another example of a lens array that is a microlens assembly.

FIG. 19 is a schematic view of an external main part showing still another example of a lens array that is a microlens assembly.

[Explanation of symbols]

1 ... Lens array (microlens assembly), 2 ... Radial direction refractive index type rod lens, 3 ... Optical axis, 4 ... Light receiving area.

Claims (2)

[Claims] 1. An analysis method for analyzing the intensity distribution and / or resolution of a point image of a microlens assembly composed of a plurality of microlenses, wherein an exit pupil including wavefront aberration of each microlens is calculated, and the calculated individual After rotating the exit pupil including the wavefront aberration of the microlenses toward the center of the microlenses with respect to the optical axis of the microlens assembly, the intensity distribution of the point image of each microlens is obtained, and each microlens is obtained. A method for analyzing a microlens assembly, wherein the intensity distribution and / or resolution of the point image of the microlens assembly is obtained by using the intensity distribution of the point image of the lens. 2. An analyzing device for analyzing the intensity distribution and resolution of a point image of a microlens assembly composed of a plurality of microlenses, and a means for calculating the wavefront aberration of each microlens assembly and the calculated wavefront aberration. Means for coordinate conversion into wavefront aberration with respect to the optical axis of the microlens assembly; means for Fourier transforming the coordinate-converted wavefront aberration of each microlens to obtain the intensity distribution of the point image of each microlens; Means for obtaining the intensity distribution of the point image of the microlens aggregate by adding the intensity distribution of the point image of the microlens, and Fourier-transforming the absolute value of the intensity distribution of the point image of the microlens aggregate to the square. An apparatus for analyzing a microlens assembly, comprising: means for determining the resolution of the microlens assembly.