JPS5850336B2 - optical low pass filter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an optical low-pass filter using a birefringent plate such as quartz crystal.

It is generally known that birefringent materials such as quartz can be used as low-pass filters, although they vary depending on the thickness of the material and other factors.

That is, when the object 1 is imaged through the optical lens system 2 as shown in FIG. 1, if the birefringence plate 3 is interposed in the imaging light beam of the lens system 2, the extraordinary ray LE becomes different from the image 4A due to the ordinary ray Lo. The image 4B is formed in a state shifted by ΔW in the horizontal force direction.

The birefringent plate 3 shown in FIG. 1 is used with its optical axis Q being tilted parallel to the horizontal force direction of the image screen.

FIG. 2 is a general explanatory diagram showing the birefringence phenomenon of a birefringent plate, and the names of each part will be added first.

However, the example shown is a case where the birefringent plate is cut along the thickness d and the force direction.

Q is the optical axis specific to the birefringent plate, nl is the refractive index in the direction of the optical axis force, n2 is the refractive index for extraordinary rays in the direction perpendicular to the optical axis, and △W is the difference between the ordinary ray Lo and the extraordinary ray LE. The separation distance, α, is the angle between the extraordinary ray LE and the ordinary ray LO, and β is the angle between the optical axis Q and the incident ray.

Here, the angle α between the extraordinary ray LE and the ordinary ray LO is given by the following, and this tanα takes the maximum value of 2 when tanβ−0/.

In the case of crystal, the difference between n and n2 is about 0.5%, so the angle α is maximum when β-45°.

Therefore, when a light beam is incident at an angle of 45° to the optical axis Q, the maximum separation distance ΔW can be obtained with the minimum thickness d, so β is generally selected to be 45°.

By the way, the fact that the subject 1 is imaged optically shifted by ΔW is caused by electrically considering this when a delay circuit 5 is provided between the input and output terminals 6a and 6b as shown in FIG. is equal to the relationship between delayed and non-delayed outputs.

Therefore, in this example, the time τ corresponding to ΔW is selected as the delay time.

Then, the transfer function R(f) of the circuit shown in FIG. 2 is expressed as follows.

In other words, the amplitude becomes cos 2πf-, and This means that an output delayed by a certain amount is obtained from the circuit 5.

Let's consider the response of imaging in the optical system shown in Figure 2, similar to the electrical signal.

In the case of space, the response in the horizontal force direction is exactly the same as It can be expressed as

Therefore, this equation (2) can be illustrated as shown in FIG. 4.

And the atmosphere point of R(u) is given by.

As is clear from equations (2) and (3) and Figure 4, the range O≦uo 1 (the diagonal line in Figure 4 indicates 2
△W Indicates.

), the birefringent plate 3 described above can be used as a low-pass filter.

The cutoff frequency of this low-pass filter is given by □.

2△W In this way, the birefringent plate 3 can be used as a low-pass filter, and within the range of 0≦uo<
W It is being used.

By the way, in the low-pass filter using this birefringent plate 3, the response R(u) in the horizontal force direction is COS
Since it is a curve, ■ Trap point draw o= Even above is not enough 2△
In order to have W sponse, this birefringent plate 3 is connected to a charge coupled device (
When used in the optical system of a solid-state imaging device using a solid-state imaging body such as a CCD (CCD), the following disadvantages arise.

For example, when a CCD is used as an imaging device, input light information corresponding to the size of a subject to be imaged is obtained from the CCD as an output signal sampled for each pixel.

That is, the sampling frequency is now f.

In this case, by scanning each pixel in each horizontal section, the output video signal obtained in one horizontal section has a sampling frequency f in addition to the modulation component SDC of the bright signal SY, as shown in FIG. .

A sideband component sM (alternating current component) in which is modulated is obtained.

However, the illustrated side only shows the fundamental wave.

In this case, the AC component sM has a sampling frequency f.

Upper and lower sidebands are generated around
During sampling frequency f.

The sideband components due to this overlap.

In other words, the shaded portion is caused by aliasing distortion.

If the image is played back in this state, a flickering phenomenon will appear on the playback screen.

Therefore, even if the birefringent plate 3 shown in FIG. 1 is used, 72;
The above components are folded back and distortion as shown by the diagonal lines in Figure 15 occurs, and the 2△W response is large, so this birefringent plate 3 cannot be used as it is as a filter for solid-state imaging devices. .

However, if the response R(u) above 2ΔW above the first trap point uo- is made as small as possible, even if there is aliasing, the component is small, so there is not much image deterioration and it can be put to practical use.

Taking these points into account, in the present invention, the same wave number characteristics in the horizontal force direction are selected so that the response after the first trap point is sufficiently smaller than the response before this trap point, and the frequency characteristics in the vertical force direction are selected. This paper proposes a flat optical low-pass filter.

Therefore, this optical filter is extremely suitable for application to the optical system in the solid-state imaging device described above.

In other words, if this optical filter is used, it is possible to avoid the effects of aliasing distortion without performing electrical processing.

The optical low-pass filter according to the present invention will be explained with reference to FIG. 6 and subsequent figures.

First, for convenience of explanation, an example will be shown in which a crystal is used as a birefringent plate and two pieces of this are used to configure an optical filter.

First, as shown in FIG. 6A, two birefringent plates 3A and 3B are
Prepare.

Although these are laminated as shown in FIG. 7, the optical axis Qa of the birefringent plate 3A located on the upper blade in this example is as shown in FIG.
It is arranged parallel to the X axis as shown in .

On the other hand, the optical axis Qb of the other birefringent plate 3B is selected to be rotated by θ (clockwise in this example) in the y-axis force direction, as shown in FIG.

Note that FIG. 6B shows a plan view of FIG. 6A.

Therefore, the optical axes Qa and Qb depicted in this figure are equal to the optical axes when projected onto the image plane.

The purpose of the following explanation is to obtain the response of the optical filter 0 shown in FIG. 7 in the horizontal force direction.

Therefore, let's first consider the polarized light components as shown in Figure 8.

This figure shows a plan view of the birefringent plate. Therefore, if we consider the incident ray as a small unit of total light flux, this ray will travel from the page toward the reader, and the extraordinary ray LE will be in the plane perpendicular to the page. Since it has an electrical displacement in the plane including the vector of E shown in , it becomes a linearly polarized light component in the X-axis force direction.

Similarly, the ordinary ray LQ is expressed as a linearly polarized light component perpendicular to this, that is, in the y-axis force direction.

Therefore, the light beam incident on the birefringent plate 3A in the upper blade is separated into an ordinary ray Lo and an extraordinary ray LF.

The separation distance is Wl. Here, if the brightness ■ of the incident light is divided into ordinary light and extraordinary light by − and the strength of the electric field of the light is E, then the brightness I of the incident light is ■−KE2 (however, K is a constant), the electric field strengths in the ordinary ray LO and the extraordinary ray LE are respectively E/.

In the following explanation, E/V7 J7 -E'.

In this way, the light rays LQ and LE obtained in a state where they are separated by Wl through the interposition of the first birefringent plate 3A are birefringent again by passing through the second birefringent plate 3B.

As mentioned above, the optical axis Qb of this birefringent plate 3B is rotated by θ in the direction of the y-axis force, so this optical axis Qb
An incident ray parallel to the axis perpendicular to Qb becomes an ordinary ray, and conversely an incident ray parallel to the optical axis Qb becomes an extraordinary ray.

Here, the ordinary ray L obtained by the first birefringent plate 3A
The strength of each electric field due to the O1 extraordinary ray LE can be divided into a CO3 component and a sine component as shown in FIG. 9A, so when it passes through the second birefringent plate 3B, the birefringence as described below arise.

That is, considering the extraordinary ray LE, **First, since the sine component is orthogonal to the optical axis Qb, it becomes the ordinary ray Lo' in the second birefringent plate 3B, and the cosine component becomes the extraordinary ray LE'.

Therefore, if the separation distance of the birefringent plate 3B is W2, the extraordinary ray LE' is the ordinary ray.

It is obtained by separating W2 directly opposite the optical axis Qb from l.

Since the ordinary ray LO is completely opposite to the above, the 5lrl component becomes the extraordinary ray LE'.

These relationships are illustrated in FIG. 9B.

Among the components thus separated, X.

Each component of the y-axis force direction (in this example, it shows the brightness of each light source)
If they are gathered on the - axis, it will be as shown in Figure 10A, so from this, the responses Rx(u) and R for both x and y axes are
y(v) can be found.

These responses Rx(u) and Ry(■) can be easily determined by applying the time axis concept as shown in FIG.

That is, if we first consider Figure 10A, this is
Considering the X-axis in Fig. 10A as the time axis, the gold input signal is at the exact center of this axis, and the transfer function of the output signal obtained by synthesizing this input through the delay and advance elements with respect to the input signal is considered equivalent.

In reality, the input signal should be considered as the right end of the axis in the diagram, but the transfer function of the output signal when this is used as the input signal is
As mentioned above, when there is one human input signal at the center of the axis, the amplitude characteristics of the transfer function of the output signal should be at least the same, so the two can be considered equivalent.

Now, input signal S i (t) is (E')2CO32πf
t, the output signal S o (t) is 5o(t) E/2sin2θ−cos2πf(t+x1)+E′2
Sin2θ・CO32πf(t+X1)+E12CO3
2θ−cos2πf(t+x2)+E′2CO32θ・
cos2 πf(t −x 2)−E'25in2θ・
CO32πft-CO32πfx, +E″CO52θ・
CO52πft-CO52πfX2 Similarly, the response Ry(v) in the y-axis force direction is Ry(v)-CO32πvy
1 ++・+・++...(5)

As described above, when two birefringent plates 3A and 3B are prepared and the optical axis Qb of the -force is rotated by θ,
Responses RX (U), Ry (v
) can be determined using equations (4) and (5) described above.

In the present invention, as described above, the configuration is such that the response after the first trap point is sufficiently smaller than the response before this trap point.

That is, in the three conventional methods using one birefringent plate, the response is as shown by curve 11 in FIG. 11, so in the present invention, for example, the response is as shown by curve 12, first trap point u
This is to reduce the response after 1.

Therefore, the cutoff point of the optical filter in this case is ul.

In this way, if at least one trap point ut exists between the first trap point u1 and the next trap point 3u1, the existence of this point ut will change the point u and subsequent responses to point l' It can be made much smaller than when there is no ul.

In the present invention, the optical axis Qb of the externally acting birefringent plate 3B is rotated in order to obtain the intermediate point u't.

Next, a specific example for obtaining the trap point ut will be described.

In the example shown below, the trap points ui are ut and 3 u.
This is a specific example of the rotation angle θ for making the rotation angle θ exist in the middle between ul and 1 (ul=2u,).

First, u-ul and u=2u1 are respectively substituted into equation (4) and rearranged.

That is, since trap points occur at u=u and u=2u1, Rx (u)=0 at that time.

Therefore, if θ in equation (8) is the desired rotation angle, and the optical axis Qb is rotated so as to satisfy equation (8), the point u2 ""' 2u will be the trap point ut.
As a result, the desired properties can be obtained.

Note that θ in equation (8) may be an angular change in any quadrant from the first quadrant to the second quadrant.

Next, let me show you a concrete example.

First, in the case of the optical filter 10 in which tan θ-1, that is, the optical axis Qb of the second birefringent plate 3B is rotated by 45 degrees clockwise with respect to the first one, a detailed explanation thereof will be omitted. (4) Each constant shown in formula 7 is as follows.

The general formula at that time can be obtained by substituting the formula (9) into the formulas (4) and (5), so the general formula can be expressed as the following formula (IOL (11)).

As is clear from the equation α0), Rx(u) is
A trap point is created at each point of 1°2u1 and 3u1.

A curve 13a in FIG. 12 shows the response expressed by equation (10) when tan θ-1.

A curve 14 in FIG. 13 shows the response of equation (11).

Furthermore, 1 to 2 examples that satisfy the above-mentioned formula (8) are shown below.
First, let's consider the case of ta"θ-fi. In this example, each constant can be determined as follows.

Rx(u) in equation (13) is shown by curve 13b in Figure 12, and the trap point in this case is ut is 8u1
and 2u1.

Next, when tanθ=v'H is selected, Rx (u
) is shown by curve 13c.

In that case, constants etc. are omitted.

In either case, it is possible to have more trap points than before, and the response after the first trap point U is smaller than the response before the first trap point 1. Therefore, when applied to a CCD However, the influence of aliasing distortion can be reduced.

By the way, as mentioned above, there are two birefringent plates 3A.

3B and rotate the -force birefringent plate 3B by θ, it is possible to create at least one trap point ui between the points u1 and 3u1, which has the advantage of reducing the response. However, in this optical filter 10, as shown in equation (5), the incident light ray is also separated in the y-axis force direction and has a response RyM in that direction, so if the image is reproduced as is, the characteristics in the vertical force direction will deteriorate somewhat. (See Figure 13).

In other words, in Figure 9B, the spatial frequency responses on the two axes that form ±α (α is an arbitrary angle →) with respect to the Y axis are different, and when viewed on the playback screen, the two axes This means that the resolution in the direction of axial force changes.

Therefore, while the image along the -force axis is reproduced in fine detail, the image along the other force axis becomes rough, resulting in an extremely unsightly image.

The present invention provides an optical low-pass filter that can take advantage of the advantages of using the two birefringent plates described above and eliminate the disadvantages described above.

In other words, in order to flatten the frequency response in the vertical force direction, that is, to make Ry(v) = O, use another birefringent plate and use this for correction of the y-axis force direction. .

In this case, in order to make the response in the y-axis force direction similar, it is sufficient to correct the ordinary ray LO' so that it reaches the X-axis where the extraordinary ray LE/ is located, as shown in FIG. 9B.

Therefore, the optical axis Qc of the third corrective birefringence plate 3C is selected to be at a position as shown in FIG.

That is, the rotation angle θ of the optical axis Qc is adjusted so that the projections of the optical axis Qc of the third birefringent plate 3C and the optical axis Qb of the second birefringent plate 3B onto a plane parallel to the imaging screen are orthogonal.
are selected.

That is, the optical filter 10 is constructed by rotating the external optical axis Qc by 90° in the third clockwise direction with respect to the optical axis Qb.

The specific relationship between these is as shown in FIG.

The output light from the second birefringence plate 3B should be the same as the output light from the optical low-pass filter using the two birefringence plates described above.

Therefore, the distribution state of the emitted light rays from the birefringent plate 3B is as shown in FIG. 9B.
The result is similar to that shown in FIG. 15A.

Among the rays separated by the second birefringent plate 3B, the ordinary ray L
When the ray o' (see FIG. 15A) passes through the third birefringent plate 3C, it is in the same direction as the optical axis Qc, so it becomes an extraordinary ray.

Therefore, now the separation distance △W of this third birefringent plate 3C is −
The third birefringent plate 3 is set so that 40 is COSθ, that is, △w−W2tanθ.
If the thickness d3 at C is selected, the ordinary ray LO' will be refracted through the third birefringent plate 3C to the position on the X-axis where the extraordinary ray LE' exists as shown in FIG. 9B. .

Contrary to the above, the extraordinary ray LE' is generated by the third birefringent plate 3.
In C, it becomes an ordinary ray, so the third birefringent plate 3C
The position of the ray does not change even after passing through.

Therefore, if the third birefringent plate 3C is provided, the component in the X-axis force direction of the light beam separated by this becomes as shown in FIG. 15B, and the component in the y-axis force direction becomes 2y1-W2S1nθ-
0, so Ry(v)-0, and the light rays are not separated in the y-axis force direction.

Therefore, by providing the third birefringent plate 3C, the optical filter 10
If configured, in addition to the feature of effectively eliminating aliasing distortion, it has a great effect of reliably preventing deterioration of resolution in the y-axis force direction, that is, in the vertical force direction in terms of the screen.

In other words, when all the separated lights are aligned on the X-axis as shown in Figure 15B, the responses on the two axes that are ±α with respect to the y-axis will be the same, and the reproduced image will look extremely natural. become.

As explained above, according to the configuration of the present invention, the frequency characteristics of the optical filter 10 are the same as the conventional ones, such as high-frequency cutoff characteristics, in other words, a low-pass filter.
If you choose the rotation angle of the optical axis, trap points u1 and 3u
Since a new trap point ut can be obtained between It has the characteristic of being a dog that can be made small.

Therefore, as mentioned at the beginning, the optical filter 10 according to the present invention is used in the optical system of a solid-state imaging device using a CCD.
If this method is used, there is no risk of image deterioration due to aliasing distortion even if the brightness variation component band is sufficiently set, so it has the characteristic that resolution can be improved with an extremely simple configuration.

Moreover, in this case, sufficient low-pass filter characteristics can be obtained in the optical system, so there is no need for an electrical processing system to remove aliasing distortion, which also simplifies the configuration of the circuit system. .

Of course, when such a circuit system is used in conjunction with the optical filter 10 described above to configure this type of solid-state imaging device,
Since aliasing distortion can be almost completely eliminated, there is an effect that even higher quality images can be obtained.

Further, in the present invention, as explained in FIG. 14 and subsequent figures, the birefringence plate 3C for correction in the y-axis force direction is used, so the response Ry (■) in the y-axis force direction is used.
Since the beam becomes completely atmospheric, there is no separation of light rays in the y-axis force direction, which has the effect of achieving the desired purpose without degrading the resolution in the vertical force direction. When used in a solid-state imaging device, it has the remarkable effect of improving the resolution in both the horizontal and vertical force directions.

In addition, in the embodiment described above, an example was described in which the optical filter 10 was constructed using three birefringent plates, but the number of birefringent plates to be used is not limited.

In the above example, the conditional expression and its specific example for obtaining the trap point ut-2u1 were described, but the point ut can be placed at any position between ul and 3u1 in almost the same way as described above. Therefore, the rotation angle of the optical axis is not limited only to equation (8).

Further, in this example, the filter is applied to a solid-state imaging device using a CCD, but it goes without saying that it is suitable for application to other imaging devices as well as other optical devices.

The birefringent plate can be made of any material other than quartz as long as it has a birefringence phenomenon.

[Brief explanation of drawings]

Figures 1 and 2 are diagrams for explaining the birefringence plate, Figure 3 is a diagram for explaining the birefringence phenomenon when considered electrically, Figure 4 is its characteristic curve diagram, and Figure 5. is a frequency spectrum diagram of the imaging signal obtained by the solid-state imaging device, No. 6
The figure shows the state of use of the birefringent plate that intercepts the optical filter, Figure 7 is the configuration of the optical filter, Figure 8 shows the direction of the electric field in the birefringent plate, and Figure 9 shows the birefringent state. Figure 10 is a diagram showing the linear polarization components in the x and y axis force directions in Figure 9, Figure g11 is a theoretical curve diagram showing the response in the X axis force direction, Figure 12 is the optical axis FIG. 13 is a curve diagram showing the response in the y-axis force direction at one rotation angle, and FIG. 14 is an example of the optical low-pass filter according to the present invention. The configuration diagram shown in FIG. 15 is the 10th block diagram in that case.
It is a figure similar to the figure. 10 is an optical low-pass filter, 3A to 3C are birefringent plates, Qa-Qc are optical axes, θ is a rotation angle, Δw, W1. W2
is the separation distance, Lo and Lol are the ordinary rays, LE·LE/ are the extraordinary rays, and d1 to d3 are the thicknesses.

Claims (1)

[Claims] 1. It has at least first to third birefringent plates, each birefringent plate has an optical axis in the same direction with respect to its surface, and the second birefringent plate has an optical axis in the same direction with respect to its surface. When the normal to the surface is the central axis,
A predetermined angle θ (−1
At the same time, the third birefringent plate is rotated in a direction perpendicular to the second birefringent plate when the normal to its surface is the central axis. the second birefringent plate so that the separated light beams, which are the output lights of the third birefringent plate, are all aligned on a line parallel to the projection axis of the optical axis of the first birefringent plate onto the surface. and an optical low-pass filter in which the thickness of the third birefringent plate is selected.