JP2000338385A - Automatic focusing device and focusing method thereof - Google Patents

Abstract

(57) [Problem] To provide an automatic focusing device and a focusing method capable of performing a focusing operation at high speed with a simple configuration. An automatic focusing apparatus includes an AF lens 101A that forms an image of subject light without correcting chromatic aberration, a photographing lens 101B that forms an image of subject light by correcting chromatic aberration, and an AF unit.
The photographing / AF switching device 113 for switching to the AF lens 101A in the imaging for normal imaging and the photographing lens 101B in the normal imaging, and the blurring characteristic information for each color in the image data of the AF area of the color image sensor 103. Calculate the point image radius, based on the calculated point image radius of each color, the distance direction calculation unit 111 that estimates the direction of the focal point and the distance to the focal point, based on the estimated distance to the focal point, It is determined whether or not the camera is in focus. If it is determined that the camera is not in focus, the focus adjustment driving device 112 moves the color image sensor 103 in the direction of the estimated focus by the distance to the focus. And

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an automatic focusing device and a focusing method thereof, and more particularly, to an automatic focusing device applied to an image input device using an image pickup device such as a video camera and a digital camera. It relates to the focusing method.

[0002]

2. Description of the Related Art With the intensification of the digital camera market in recent years, cost reduction has been required and reduction of the number of parts has become an important issue. In such an environment, a microprocessor (including a DSP) is one of the main components of a digital camera. However, recent microprocessor processors have reached a level of performance far exceeding the processing capability of a digital camera controller at a low price. I have. For this reason, for example, in a digital camera, the function of a distance measuring module (AF sensor) component of a silver halide camera is being replaced with an imaging system + digital signal processing. As a focusing method of a digital camera, there are mainly a "hill climbing method" and a "correlation method". Hereinafter, the "hill climbing method" and the "correlation method" will be described.

In the focusing method based on the generally known “hill climbing method”, an AF evaluation value (calculated from a high frequency component of an image) at an image capturing position can be obtained. It is difficult to detect in which direction the focal point is located and at what distance the focal point is located. Therefore, in order to detect the in-focus position while avoiding the local maximum point, the AF evaluation value of the entire lens moving range is required. In addition, there is a problem that it takes time to obtain an accurate focus position.

The "correlation method" includes an autocorrelation method and a cross-correlation method. First, in the focusing method based on the autocorrelation method, two or more different light beams are imaged in one frame. However, while focus information can be obtained from a captured image of one frame, correlation based on the same data is obtained. Therefore, the result shows a very high peak value at the origin position (focal point) of the autocorrelation coefficient. Therefore,
Since the AF information is buried by the peak value near the focal point, it is difficult to detect the focal point near the focal point, and there is a problem that the focal point must be detected by another method near the focal point.

On the other hand, in the focusing method based on the cross-correlation method, 2
Although imaging is performed for each of the AF areas for two different light beams, it is necessary to prepare two image memories, but this does not cause a very high peak value at the origin position unlike the autocorrelation method. From this, focus information can be obtained from the vicinity of the focal point to the distance without being buried in this peak value. However, in the cross-correlation method, it is necessary to prepare two different light beams with an AF diaphragm to obtain focus information, and there is a problem that the AF diaphragm is not required at the time of photographing. In addition, the aperture plate for AF has a fixed opening size, and it is difficult to optimize the amount of light received by the image sensor.

There has also been proposed a method of detecting a focal point using chromatic aberration of subject light. For example, Japanese Unexamined Patent Publication
An "autofocus device" described in JP-A-138362 includes a lens having a predetermined chromatic aberration, imaging means for imaging a subject via the lens, and an amplitude value of a color signal output from the imaging means. Value detection means for detecting the focus position information when the subject is imaged by the lens based on the detection result of the amplitude value detection means; and The color signal is corrected by convolving the inverse function of the point spread function to reproduce the image of the subject formed on a virtual plane separated by a predetermined distance from the imaging plane used for imaging the color signal. Means.

[0007] An "autofocusing device" described in Japanese Patent Application Laid-Open No. 10-200904 forms an image of a subject on an image pickup device by an image pickup lens, and adjusts a contrast value of a video signal read from the image pickup device. In the automatic focusing apparatus for controlling the position of the imaging lens based on the image signal, one of the plurality of color signals included in the video signal is preferentially used, and the in-focus position related to the one color signal is used for the imaging. The imaging lens is moved so as to appear earlier than a predetermined focal plane of the lens, and the imaging lens is moved in the same direction by a predetermined distance from the imaging lens position where the contrast value of the one color signal has a maximum value. To end the focusing operation.

An "autofocus device" described in the above-mentioned Japanese Patent Application Laid-Open No. 06-138362,
"Automatic focusing device" described in JP-A-200904
Has an advantage that the convergence to the focal point is faster than that of the “hill-climbing method” because the direction of the focal point is immediately detected using chromatic aberration.

[0009]

However, there is a problem with the "autofocus device" described in the above-mentioned JP-A-06-138362 and the "autofocus device" described in the JP-A-10-200904. Since the distance to the focal point is not detected, it is necessary to take images for focusing many times before the focal point is reached. There is a problem that it takes time to obtain

The present invention has been made in view of the above, and an object of the present invention is to provide an automatic focusing apparatus capable of performing a high-speed focusing operation with a simple configuration and a focusing method thereof.

[0011]

In order to solve the above-mentioned problems, the invention according to claim 1 forms an image of a subject light without correcting chromatic aberration in the imaging for AF, and forms the subject light in the normal imaging. A lens system configured to form an image by correcting chromatic aberration, an AF area in which an AF area is set in a central portion of an imaging area, and a color image sensor that converts a subject image formed by the lens system into image data, and image data of the AF area Focus position estimating means for estimating the direction of the focal point and the distance to the focal point based on the calculated blur characteristic information of each color, and estimating by the focus position estimating means. Focusing state determining means for determining whether or not the camera is in a focus state based on the distance to the focused focal point; and Estimated by position estimation means Distance to the focus point in the direction of the focus point that, a driving means for moving the lens system or the color image sensor, in which with a.

According to a second aspect of the present invention, there is provided a first lens which forms an image by correcting chromatic aberration of subject light and causing chromatic aberration on an optical axis so as to have different focal lengths for a plurality of visible light wavelengths. A second lens disposed so that a focal position of any one color in the visible light wavelength band becomes the same focal position as the first lens, and an AF in the first lens in normal imaging. Lens switching means for switching to the second lens, and AF at the center of the imaging area.
A color image sensor for converting an object image formed by the first or second lens system into an image data in which an area is set, and a point image distribution showing a blur characteristic for each color of the image data in the AF area Calculate the coefficients, calculate the point image radius of each color based on the calculated point image distribution coefficient of each color, and estimate the direction of the focal point and the distance to the focal point based on the calculated point image radius of each color. Position estimating means, based on the distance to the focal point estimated by the in-focus position estimating means,
Focusing state determining means for determining whether or not the camera is in focus;
When the in-focus state determining unit determines that the camera is not in the in-focus state, the lens system or the color imaging device is moved by the distance to the in-focus point in the direction of the focal point determined by the in-focus position estimating unit. And a driving means for moving.

The invention according to claim 3 switches between a first mode in which the subject light is formed by correcting the chromatic aberration and forming an image, and a second mode in which the subject light is formed without correcting the chromatic aberration by the lens arrangement. Lens switching means for switching the lens group to the first mode for normal imaging and moving the lens group to the second mode for AF imaging by moving the lens group; An AF area is set at a central portion of the imaging area, a color image sensor that converts a subject image formed by the lens group into image data, and a point image showing blur characteristics for each color of the image data in the AF area The distribution coefficient is calculated, the point image radius of each color is calculated based on the calculated point image distribution coefficient of each color, and the direction of the focal point and the distance to the focal point are estimated based on the calculated point image radius of each color. Focus Estimating means, focusing state determining means for determining whether or not the camera is in focus based on the distance to the focal point estimated by the focusing position estimating means, and focusing by the focusing state determining means If it is determined that it is not in the state,
And a driving unit for moving the lens system or the color image pickup device in the direction of the focal point estimated by the focal position estimating unit by a distance to the focal point.

According to a fourth aspect of the present invention, in the automatic focusing apparatus according to the second or third aspect, the in-focus position estimating means multiplies the image data of the AF area by a window function. The point image distribution coefficient is calculated by performing two-dimensional Fourier transform to convert into the amplitude and phase in the frequency domain, replacing each phase in the entire frequency domain with zero, and performing two-dimensional inverse Fourier transform.

The invention according to claim 5 is the invention according to claims 2 to
5. The automatic focusing device according to claim 4, wherein the focus position estimation unit calculates a cross-sectional area based on a threshold calculated based on an origin peak value of the point spread coefficient. The point image radius is calculated based on the calculated sectional area.

According to a sixth aspect of the present invention, there is provided a focusing method of an automatic focusing device for performing an automatic focusing operation by moving a lens system or a color image pickup device.
A first step of forming an image of the subject light without correcting the chromatic aberration, and an AF of the subject image formed on the color image sensor.
Calculate blur characteristic information for the image data of the area for each color,
A second step of estimating the direction of the focal point and the distance to the focal point based on the calculated blur characteristic information for each color, and determining whether the object is in focus based on the estimated distance to the focal point. A third step of determining whether or not the lens is in focus, and if it is determined that the lens is not in focus, the lens is moved by the distance to the focus in the estimated direction of focus. A fourth step of moving the system or the color image sensor, and moving the lens system or the color image sensor by the distance to the focal point in the direction of the estimated focal point, Steps ~
A fifth step of repeating the third step;
A step of performing chromatic aberration correction on the subject light by the lens system to form an image on the color image pickup device and performing normal photographing when it is determined in step that the object is in focus. It is a thing.

According to a seventh aspect of the present invention, there is provided a focusing method of an automatic focusing apparatus for performing an automatic focusing operation by moving a lens system or a color image pickup device.
A first step of forming an image of the subject light without correcting the chromatic aberration, and an AF of the subject image formed on the color image sensor.
The point image distribution coefficient indicating the blur characteristic is calculated for each color of the image data of the area, the point image radius of each color is calculated based on the calculated point image distribution coefficient of each color, and based on the calculated point image radius of each color, A second step of estimating a direction of the in-focus point and a distance to the in-focus point, a third step of determining whether or not the subject is in focus based on the estimated distance to the in-focus point; In the third step, when it is determined that the object is not in focus, the lens system or the color image pickup device is moved in the estimated direction of the focus by a distance to the focus. Step and in the direction of the estimated focal point by the distance to the focal point,
A fifth step of repeating the first to third steps after moving the lens system or the color image pickup device, and a case where it is determined in the third step that the object is in focus. A sixth step of correcting chromatic aberration of subject light by the lens system, forming an image on the color image sensor, and performing normal photographing.

According to an eighth aspect of the present invention, in the focusing method of the automatic focusing apparatus according to the seventh aspect, the second step includes multiplying the image data of the AF area by a window function. The point spread coefficient is calculated by performing a two-dimensional inverse Fourier transform after converting each phase of the entire frequency domain to zero by performing a dimensional Fourier transform to convert the phase and the phase into an amplitude and a phase in the frequency domain.

According to a ninth aspect of the present invention, in the focusing method of the automatic focusing apparatus according to the seventh or eighth aspect, the second step includes the step of: A cross-sectional area is calculated based on a threshold calculated based on the calculated cross-sectional area, and the point image radius is calculated based on the calculated cross-sectional area.

[0020]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS With reference to the accompanying drawings, preferred embodiments in which an automatic focusing apparatus according to the present invention is applied to a digital camera will be described below (Principles of the Invention), (Embodiment 1), Embodiment 2 will be described in detail.

(Principle of the Invention) First, the principle of the present invention is shown in FIG.
This will be described with reference to FIGS. FIG. 1 is an explanatory view for explaining the principle of the present invention, and FIG. 2 is an AF of a color image sensor.
FIG. 3 is an explanatory diagram for explaining an area, FIG. 3 is an explanatory diagram for explaining a method of determining the direction and distance of a focal point, and FIG. 4 is a diagram for explaining a relationship between a point image radius and a stop aperture diameter.

In FIG. 1, 101A denotes an AF lens without chromatic aberration correction, 102 denotes an imaging stop, and 103 denotes a color image sensor. Rg indicates the radius of the point image of G color. FIG. 3 shows the optical path of the RGB light, and shows a case where the color image sensor 103 is at a position to be a rear focus and a case where it is at a position to be a front focus. In the figure,
The light incident from the left to the right is AF without chromatic aberration correction.
After passing through the imaging aperture 102 through the imaging lens 101A,
Light is received by a color image sensor 103 having a color filter. In this case, what is needed as the focus information is image data of an area (AF area) that the photographer wants to focus on.
Only the image data of the area is transferred.

FIG. 2 shows the AF of the color image sensor 103.
FIG. 4 is a diagram showing an area, and as shown in the figure, an AF area is set at a center position of an optical axis of an optical system in a frame of the color image sensor 103. In the present invention, since the color image sensor 103 is configured to enable random access of pixels, the transfer target is only the data in the AF area, and the transfer time is greatly reduced.

Thereafter, for the RGB image data separated for each color by the color filter of the color image sensor 103, a point spread coefficient of the image data of the AF area is obtained for each color. FIG. 3 shows an example of point image distribution coefficients of R, G, and B colors in the case of front focus (A), focus (B), and rear focus (C).

FIG. 4 is a diagram showing the relationship between the point image radius and the stop aperture diameter. In the figure, the horizontal axis indicates the color image sensor position (or lens position), and the vertical axis indicates the point image radius. As shown in the figure, the larger the aperture opening diameter, the larger the point image radius, and the smaller the point image radius at the in-focus position, which affects the point image radius in proportion to the degree of the aperture. .

The distance to the focal point is estimated from the point image distribution coefficient of the image data of the AF area for each color, information on the aperture diameter of the aperture and the distance of the light receiving surface of the aperture surface, and the point image radius Rg of the G color image. , The in-focus direction (front focus or rear focus) is estimated from the magnitude relationship between the three point image radii of the RGB color images. Here, the case where the focal position of the G color image is selected as the target focal length is shown.

(Embodiment 1) FIG. 5 shows a configuration diagram of an AF processing system of a digital camera according to Embodiment 1. In FIG. 1, reference numeral 101A denotes an AF lens, and a subject image of a subject to be focused is taken by a color image sensor 10;
3 for forming an image on the surface 3 and not correcting the chromatic aberration at a plurality of visible light wavelengths (for example, RGB colors). Reference numeral 101B denotes a photographing lens, and a subject image of a subject to be focused is taken by a color image sensor 10B.
3 for chromatic aberration correction. The AF lens 101A is configured such that the focal position of one color (for example, G color) in the visible light wavelength band is the same as the focal position of the imaging lens 101B. Reference numeral 102 denotes an imaging diaphragm, which is disposed on the rear side of the AF lens 101A and the photographing lens 101B, and restricts a light beam (light amount) passing through the AF lens 101A and the photographing lens 101B.

Reference numeral 103 denotes a color image sensor (primary color type) comprising a color CCD or the like which converts a formed subject image into an electric signal and outputs it as image data. The color image sensor 103 can perform random access of pixels, and can transfer image data of an arbitrary area in an image frame. These AF
Lens 101A, photographing lens 101B, photographing aperture 1
02 and the color image sensor 103 constitute an imaging optical system. An automatic exposure control unit 104 performs automatic exposure control by adjusting the aperture of the shooting aperture 102.

Reference numeral 105 denotes an AF area image data memory for storing image data (RGB data) of the AF area in each image frame picked up by the image pickup for AF. 1
Reference numeral 20 denotes a point spread coefficient calculator for calculating a point spread coefficient of the image data stored in the AF area image data memory 105. The point image distribution coefficient calculation unit 120 adds two points to the image data stored in the AF area image data memory 105.
A window function multiplication unit 106 that multiplies the two-dimensional window function by the two-dimensional window function
A two-dimensional FFT unit 107 for performing a two-dimensional Fourier transform, a phase operation unit 108 for performing a phase operation on the data subjected to the Fourier transform by the two-dimensional FFT unit 107, and a two-dimensional inverse Fourier transform And a two-dimensional IFFT unit 109 for calculating a point spread coefficient.

Reference numeral 110 denotes a point spread coefficient memory for storing the point spread coefficient for each color calculated by the point spread coefficient calculator 120. Reference numeral 111 denotes a distance direction calculation unit that calculates the direction and the distance to the in-focus position of the color image sensor 103 based on the point image distribution coefficient for each color calculated by the point image distribution coefficient calculation unit 120.

Reference numeral 112 denotes a focus adjustment drive mechanism for moving the color image sensor 103 back and forth based on the calculation result of the distance direction calculation unit 111. Reference numeral 113 denotes an AF lens 101A and an AF lens for normal shooting. Lens 1
01B shows a photographing / AF switching device that switches between 01B and 01B. 11
Reference numeral 4 denotes a frame image memory in which image data of one frame that has been imaged is stored for each color in normal shooting.

Here, the color image sensor 1
Although the focus adjustment is performed by moving the lens 03 in the optical axis direction, a configuration in which the focus adjustment is performed by moving the AF lens 101A instead of moving the color image sensor 103 may be adopted. .

Next, the AF of the digital camera shown in FIG.
The operation and the photographing operation will be described with reference to FIGS. 9 to 14 according to the flowcharts of FIGS. FIG. 6 shows AF
Flowchart for explaining the operation and the photographing operation,
FIG. 7 is a flowchart for explaining the point image radius calculation processing of the AF operation in FIG. 6 in detail, and FIG. 8 is a flowchart for describing the focal length direction calculation processing of the AF operation in FIG. 6 in detail.

FIG. 9 is an explanatory view for explaining a two-dimensional Hamming window function, FIG. 10 is an explanatory view for explaining a point spread coefficient at the time of focusing, and FIG. 11 is an explanatory view of a point spread coefficient at the time of out-of-focus. FIG. 12 is an explanatory diagram for explaining a method of calculating a point image radius, FIG. 13 is an explanatory diagram for explaining a focal length L at the time of front focus, and FIG. 14 is a focal length at the time of rear focus. L
FIG.

In the flowchart of FIG. 6, first, in the digital camera shown in FIG.
When a shutter button (not shown) is half-pressed, the imaging optical system of the digital camera operates as an AF sensor. Then, when the AF sensor operates, the photographing / AF switching device 113 arranges the AF lens 101A (lens without chromatic aberration correction) on the optical axis (step S10).
1). The exposure control unit 104 also controls the imaging stop 1 of the optical system.
Using 02, exposure control is performed so that the amount of light of the subject incident on the image sensor from the outside is always optimal. In this state, shooting for AF is performed (step S10).
2) The image data of the AF area (see FIG. 2) on the color image sensor 103 is transferred to the AF area image data memory 105 for each of RGB, and the AF area image data memory 105 stores the image data of the AF area for each of RGB. It is stored (step S103).

Next, a point image radius R is calculated for each color based on the image data of each color component (R, G, B) stored in the image memory 105 for the AF area (step S10).
4-S108). As a method of calculating the point image radius R, a method of calculating using the Fourier transform will be described below.

First, the point spread coefficient calculator 120 calculates A
Based on the image data of each color component (R, G, B) stored in the F area image data memory 105, each color (R, G, B)
G, B), the point spread coefficient is calculated. Specifically, the window function multiplying unit 106 reduces the influence of the high frequency component at the image boundary on the image data f ₀ (u, v) in the AF area as shown in the following equation (1), for example: A two-dimensional window function w (u, v) such as a Hamming window as shown in FIG. 9 is multiplied (step S104).

F (u, v) = w (u, v) · f ₀ (u, v) (1) where w (u, v) = w (u) · w (v) w ( u) = 0.54 + 0.46 · cos (2πu / N) w (v) = 0.54 + 0.46 · cos (2πv / N) N: Image size

Next, the two-dimensional FFT unit 107
A two-dimensional discrete Fourier transform DFT (actually, a fast Fourier transform FFT is performed) is performed on (u, v) to obtain frequency domain data F (U, V) (step S105).

When the point spread coefficient in the frequency domain is a complex number H (U, V), the phase operation unit 108 calculates the image data in the frequency domain in order to obtain the H (U, V). Each phase of F (U, V) is replaced with zero (step S106). That is, as shown in the following equations (2) and (3), the amplitude of F (U, V) is set to the real part of H (U, V) and H (U, V).
The imaginary part of V) is set to zero.

Re {H (U, V)} = | F (U, V) | (2) Im {H (U, V)} = 0 (3) where | F (U , V) | = {[Re {F (U, V)} ² + Im
{F (U, V)} ² ]

The two-dimensional IFFT section 109 performs a two-dimensional inverse discrete Fourier transform IDFT (actually, performs an inverse fast Fourier transform IFFT) on the result to obtain a point image distribution coefficient h (u, v). ) (Step S1)
07) Then, the point spread coefficient h (u, v) calculated for each color (R, G, B) is stored in the point spread coefficient memory 110.

The distance direction calculation unit 111 calculates a point image radius R for each color based on the point image distribution coefficient h (u, v) of each color.
(The point image radius of the R color is Rr, the point image radius of the G color is Rg, and the point image radius of the B color is Rb) (step S10).
8). A specific method of calculating the point image radius R will be described with reference to the flowchart of FIG. Note that the point spread coefficient h (u, u,
v) indicates a peak value at the origin. FIG. 10 shows an example of the point spread coefficient obtained from the focused image, and FIG. 11 shows an example of the point spread coefficient obtained from the blurred image. As shown in FIGS. 10 and 11, the distribution of the point spread function of the focused image has an impulse shape, and the distribution of the point spread function of the blurred image has a gentle cone shape according to the degree of blur.

Referring to FIG. 7, for example, an origin peak value of an impulse shape or a conical shape is input (step S201).
A sectional threshold is calculated based on the peak value of the origin (step S202). For example, as shown in FIG. 6, the sectional area of the point spread coefficient obtained by slicing the point spread coefficient by the calculated sectional threshold (cross sectional pixel) Calculate S) (Step S20)
3). Specifically, as shown in FIG. 6A, the cross-sectional area S is calculated by counting the number of pixels corresponding to the cross-section. In the example shown in the figure, the cross-sectional area S is “52”. Then, based on the calculated sectional area S, the following equation (4)
Is calculated (step S204), and the calculated point image radius R is output (step S205). In the example shown in FIG. 6B, the point image radius R is “4”.

R = √ (S / π) (4) where π: pi

Subsequently, in FIG. 15, after calculating the point image radius R for each color, the distance direction calculator 111 determines the focal direction and calculates the focal length L (step S10).
9). With reference to FIG. 8, a method of determining the focal direction and calculating the focal length will be specifically described. Here, the case where the focal position of the G color image is selected as the target focal length will be described.

The distance direction calculation unit 111 estimates the direction of the focal point by judging the magnitude relation of the point image radii Rr: Rg: Rb of the RGB image, and further calculates the distance to the focal point according to the focal direction. presume.

More specifically, when the input of Rr: Rg: Rb, the input of the aperture opening Ro, and the input of the aperture light receiving surface Lo of the radius of each point image of the RGB color image are performed (step S30).
1) The magnitude relation of the point image radii Rr: Rg: Rb of the RGB color image is determined (step S302). Rr <Rg <
In the case of Rb, the process shifts to step S303 to estimate the front focus (step S303), and for the focal length L, information on the aperture opening diameter Ro, the aperture surface light receiving surface distance Lo, and the point image radius of the G color image Based on Rg, the focal length L (the distance to the in-focus point of the color G of the color image sensor 103) is calculated by the following equation (5). FIG. 13 is a diagram illustrating an example of the focal length L at the time of front focus.

L = Lo · Rg / (Ro + Rg) (5)

In step S302, Rr>
If Rg <Rb, the process proceeds to step S304,
It is estimated that the subject is in focus and the focal length L = 0 (step S)
307).

In step S302, Rr>
If Rg> Rb, the process proceeds to step S305,
The focal length L is estimated based on the rear focus, and the focal length L is calculated by the following equation (5) based on the information of the aperture diameter Ro, the aperture surface light receiving surface distance Lo, and the point image radius Rg of the G color image. FIG.
FIG. 7 is a diagram illustrating an example of a focal length L at the time of back focus.

L = Lo · Rg / (Ro−Rg) (6)

Then, the calculated focal length L is output (step S309). Subsequently, the process proceeds to step S110 in FIG. 6, and the focus drive control device 112 determines whether or not the subject is in focus based on the calculated focal length L (the light receiving position of the color image sensor 103 and the AF lens). 1
It is determined whether or not the focal point of 01A is coincident). If the focal point is not in the in-focus state, the color image sensor 103 (or the AF lens 101A) is moved to the focal position (only the focal length L in the calculated focal position direction). (Step S111), the process returns to Step S102, and the same AF process is repeated once again to determine whether the camera has reached a true focus position (focused state). The same AF processing is performed until the focusing state is achieved (step S10).
2 to step S111) are repeated.

On the other hand, if it is determined in step S110 that the object is in focus, the photographing / AF switching device 113 switches between the AF lens 101A and the photographing lens 101B.
The photographing lens 101B is arranged on the optical axis (step S1).
12), the preparation for photographing the subject is completed, and the system is in a state of waiting for the shutter button to be fully pressed. Thereafter, when the shutter button is fully depressed, the shutter is opened for a certain period of time in conjunction therewith, and light from the subject is transmitted to the color image sensor 10.
Light is received at 3. The image data from the image sensor 103 is stored in each frame image memory (R / G /
B) The data is transferred to 114, and these data are stored or displayed on a monitor after image processing such as white balance (step S113).

Note that the number of AF operations is determined by the color image sensor 103 (or the AF lens 101A).
In the case where the movement start position is near the in-focus position, the point spread coefficient shows a sharp peak as shown in FIG. The focus position is reached within the allowable range by the AF operation. On the other hand, if the movement start position of the color image sensor 103 (or the AF lens 101B) is far from the focus position, in order to obtain focus information from a blurred image,
The point spread coefficient shows a gradual peak as shown in FIG. 11, and reaches the allowable range of the focus position by a plurality of AF operations.

As described above, in the first embodiment, the AF area is set at the center of the image pickup area (image pickup frame) of the color image sensor 103, and a plurality of visible areas are set for the image pickup for AF. After imaging a subject with a lens (AF lens 101A) that does not correct chromatic aberration at a light wavelength (for example, RGB color), blur characteristic information (point image distribution coefficient) for each color of the AF area image data on the color image sensor 103 ), The distance and direction to the focal point are estimated, and after moving the AF lens 101A or the color image sensor 103 so that the light receiving position of the color image sensor 103 and the focal point of the AF lens 101A coincide with each other, Imaging lens 1 with corrected chromatic aberration
Since shooting of the subject is performed at 01B, information on the distance and direction to the focal position can be obtained only by one imaging for AF, and it is possible to focus quickly. Further, it becomes possible to focus on the subject by following the movement of the subject.

In the first embodiment, the focal direction is determined by comparing the point image radii of the respective colors, so that the focal direction is determined based on the magnitude of the high-frequency component by a filter method. As compared with the method, there is an effect that the color component of the subject is less affected.

Further, in the first embodiment, chromatic aberration is generated on the optical axis so as to have different focal lengths for a plurality of visible light wavelengths with respect to the photographing lens 101B whose chromatic aberration has been corrected. And an AF lens 101A arranged so that the focal position of a certain color (for example, G color) has the same focal position as the photographing lens 101B. In the AF operation, a frame imaged through the AF lens 101A is provided. Of the AF area, obtains a point spread coefficient indicating a blur characteristic for each color of the image data of the AF area, calculates a point spread radius of each color based on the point spread coefficient of each color, and calculates a point spread of each color. The distance and direction from the radius to the focal point are estimated, and the light receiving position of the color image sensor 103 and the AF lens 1 are determined based on the calculated distance to the focal point.
It is determined whether or not the focal point of 01A matches, and if it is determined that the focal points do not match, the AF lens 101A or the color image sensor 103 is moved according to the calculated distance and direction to the focal point, and When it is determined that the focal points match, it is decided to switch to the photographing lens 101B to perform normal photographing of the subject, so that information on the distance and direction to the focal point is obtained only by one image pickup for AF. And focus can be quickly achieved. Further, it becomes possible to focus on the subject by following the movement of the subject. Further, the AF lens 101A and the photographing lens 1
It is possible to perform imaging for AF and normal imaging with a simple configuration for switching 01B.

In the first embodiment, as a method of calculating the point spread coefficient, image data in the AF area is multiplied by a window function, and then converted into amplitude and phase in the frequency domain by two-dimensional Fourier transform. After replacing each phase in the entire frequency domain with zero, two-dimensional inverse Fourier transform is performed to obtain a point spread coefficient. Therefore, DFT (discrete Fourier transform) and FFT (fast Fourier transform) can be applied.
It is suitable for digital integrated circuits such as SP (Digital Signal Processor).

Further, in the first embodiment, distance direction calculating section 111 calculates a cross-sectional area based on a threshold value calculated based on the peak value of the point spread coefficient at the origin, and calculates a point based on the cross-sectional area. Since the image radius is obtained, even when the point image cross-section is a polygon that does not become circular, such as an aperture opening of an actual camera, the point image radius in the case of approximating a circle can be obtained. The image radius can be easily and accurately calculated.

(Embodiment 2) Embodiment 2 is described with reference to FIGS.
This will be described with reference to FIG. FIG. 15 is a configuration diagram of an AF processing system of the digital camera according to the second embodiment. In the first embodiment (see FIG. 1), the AF lens 101A and the photographing lens 101B are separately prepared on the central axis of the photographing optical system, and the AF lens 101A is used at the time of AF and at the time of photographing.
In the second embodiment, a configuration in which chromatic aberration correction is performed and a state in which chromatic aberration is not corrected due to a difference in arrangement of lens groups will be described. Other configurations are described in Embodiment 1.
Therefore, description of common parts is omitted. still,
In FIG. 15, the same parts as those in FIG. 1 are denoted by the same reference numerals.

In FIG. 15, reference numeral 101 denotes a photographing and AF lens, which has chromatic aberration correction and no chromatic aberration correction depending on the arrangement of the lens groups (low dispersion material (lens) and high dispersion material (lens)). The state can be switched. The photographing / AF switching device 113 arranges the lens group of the photographing / AF lens 101 so as to be in a state without chromatic aberration correction during AF, and to be in a state with chromatic aberration correction during photographing.

Next, the function of the photographing and AF lens 101 will be described with reference to FIGS. FIG. 16 shows the lens arrangement of the imaging and AF lens 101 when chromatic aberration correction is not performed, and FIG. 17 shows the relationship between the focal length and the color wavelength in the case of the lens arrangement of FIG. 16 (when chromatic aberration correction is not performed). 18 shows the lens arrangement when the chromatic aberration of the photographing and AF lens 101 is corrected, and FIG. 19 shows the relationship between the focal length and the color wavelength in the case of the lens arrangement of FIG. 18 (when the chromatic aberration is corrected).

FIG. 16 shows a low-dispersion material (lens) 2 of the photographing and AF lens 101 when the target focal length is different depending on the color wavelength (R, G, B) as shown in FIG.
1 shows an example of the arrangement of a high dispersion material (lens) 202. As shown in FIG. 16, when the photographic / AF lens 101 is not to be subjected to chromatic aberration correction, the distance between the low dispersion material (lens) 201 and the high dispersion material (lens) 202 is increased.

FIG. 18 shows a low-dispersion material (lens) 201 and a high-dispersion material of the lens for shooting and AF 101 such that the target focal length is the same for each color wavelength (R, G, B) as shown in FIG. An example of the arrangement of the material (lens) 202 is shown. FIG.
As shown in (1), when the photographic / AF lens 101 is in a state of correcting chromatic aberration, the distance between the low dispersion material (lens) 201 and the high dispersion material (lens) 202 is reduced. If the target focal length cannot be attained due to the arrangement of the optical lens, the correction may be performed on the AF processing device side.

Regarding the AF operation and the photographing operation,
In the image pickup for the above, the photographing / AF switching device 113 sets the arrangement of the photographing / AF lens 101 as shown in FIG. 16 (without chromatic aberration), and in the actual photographing, the photographing / AF switching device 113 The arrangement of the photographing and AF lens 101 is set as shown in FIG. 18 (a state with chromatic aberration), and the other operations are the same as those in the first embodiment (see the flowcharts in FIGS. 6 to 8). Omitted.

As described above, the second embodiment includes the photographing / AF lens 101 which can switch between a state with chromatic aberration correction and a state without chromatic aberration correction depending on the arrangement of the lens groups. Shooting for shooting A
Since the arrangement of the lens group of the F lens 101 is set to a state without chromatic aberration correction, and in the actual photographing, the arrangement of the lens group of the shooting and AF lens 101 is set to a state with chromatic aberration correction. , AF imaging and normal imaging can be performed.

It should be noted that the present invention is not limited to the above-described first and second embodiments, and can be appropriately changed without changing the gist of the present invention.

In the first and second embodiments, the digital camera has been described as an example.
It is possible to obtain information on the distance and direction to the in-focus position with only one imaging at any focal lens position, and it can be used as a tracking servo, so it can be applied to digital video cameras It is.

In the first and second embodiments, the two-dimensional discrete Fourier transform (DFT) or the fast Fourier transform (FF) is used to obtain the point spread coefficient for focus control.
Apply digital signal processing according to T). These operations may use the surplus capacity of the camera controller processor, or may include an arithmetic circuit in an integrated circuit such as an IPP (Image Pre Processor). For the window function, a part of w (u, v) may be stored as a table in order to save the calculation, and only the coefficient multiplication may be performed.

[0071]

According to the first aspect of the invention, the lens system forms an image of the subject light without correcting the chromatic aberration in the imaging for AF, and forms the image by correcting the chromatic aberration of the subject light in the normal imaging. , The color image sensor is located at the center of the imaging area.
The F area is set, the subject image formed by the lens system is converted into image data, and the focus position estimating means calculates blur characteristic information for each color of the image data in the AF area, and calculates the blur characteristic of each color. Based on the information, the direction of the focal point and the distance to the focal point are estimated, and the focus state determining means is based on the distance to the focal point estimated by the focal position estimating means.
It is determined whether or not the camera is in focus, and if the drive means determines that the camera is not in focus by the focus state determination means, the drive means moves to the in-focus direction estimated by the focus position estimation means to reach the in-focus point. Since the lens system or the color image sensor is moved by the distance described above, information on the distance and direction to the focal position can be obtained only by performing imaging for one AF operation. A focus operation can be performed.

According to the second aspect of the present invention, the first lens that forms an image by correcting the chromatic aberration of the subject light and the chromatic aberration on the optical axis so as to have different focal lengths for a plurality of visible light wavelengths are provided. And a second lens disposed so that a focal position of any one color in the visible light wavelength band is at the same focal position as that of the first lens. The first lens is switched to the second lens in the imaging for AF, and the color imaging element is set to the AF area in the center of the imaging area, and the first or second lens is set.
The in-focus position estimating means calculates a point image distribution coefficient indicating a blur characteristic for each color of the image data in the AF area, and calculates the point image distribution of each color. The point image radius of each color is calculated based on the coefficient, and the direction of the focal point and the distance to the focal point are estimated based on the calculated point image radius of each color. Based on the distance to the in-focus state, it is determined whether or not the camera is in focus. If the focus state determination means determines that the camera is not in focus, the drive position is estimated by the focus position estimation means. Since the lens system or the color image sensor is moved by the distance to the focal point in the direction of the focused focal point, information on the distance and the direction to the focal point position can be obtained only by one imaging for AF. High-speed focusing operation with a simple configuration. It becomes possible. Further, by switching between the first lens and the second lens, it is possible to perform imaging for AF and normal imaging.

According to the third aspect of the present invention, the first mode in which the subject light is imaged with chromatic aberration corrected by the lens arrangement, and the second mode in which the subject light is imaged without chromatic aberration correction. And a lens switching unit that moves the lens group to switch to the first mode for normal imaging and to the second mode for imaging for AF,
The color image sensor has an AF area set at the center of the imaging area, converts the subject image formed by the lens group into image data, and the focus position estimating means uses the blur characteristic for each color of the image data in the AF area. Is calculated, and the point image radius of each color is calculated based on the calculated point image distribution coefficient of each color. Based on the calculated point image radius of each color, the direction of the focal point and the distance to the focal point are calculated. The in-focus state determining means determines whether or not the camera is in focus based on the distance to the focal point estimated by the in-focus position estimating means. When it is determined that the camera is not in the state, the lens system or the color image sensor is moved by the distance to the focal point in the direction of the focal point estimated by the focal point position estimating means. Focus operation That. Further, by changing the arrangement of the lens groups, it is possible to perform imaging for AF and normal imaging.

According to a fourth aspect of the present invention, in the second or third aspect, the focus position estimating means multiplies the image data of the AF area by a window function.
After performing two-dimensional Fourier transform to convert into amplitude and phase in the frequency domain, and replacing each phase in this entire frequency domain with zero,
Since the point spread coefficient is calculated by performing a two-dimensional inverse Fourier transform, in addition to the effects of the invention described in claim 2 or claim 3, DFT (discrete Fourier transform) or FFT (fast Fourier transform) can be performed. Applicable, DSP (DigitalSignal P
Suitable for digital integrated circuits such as

According to the invention of claim 5, in the invention of any one of claims 2 to 4,
The focus position estimating means calculates the cross-sectional area based on the threshold value calculated based on the peak point value of the point image distribution coefficient, and calculates the point image radius based on the calculated cross-sectional area. Even if the point image cross-section is a polygon that does not become circular, as in the opening part, the radius of the point image can be obtained when the circle is approximated, and the point image radius can be calculated easily and with high accuracy. Becomes

According to the sixth aspect of the present invention, the object light is formed by the lens system without correcting the chromatic aberration, and the image data of the AF area of the object image formed on the color image pickup device is obtained for each color. The blur characteristic information is calculated based on the calculated blur characteristic information for each color, the direction of the focal point and the distance to the focal point are estimated, and the subject is in focus based on the estimated distance to the focal point. If it is determined that the camera is not in focus, the lens system or the color image sensor is moved by the estimated distance to the focus in the direction of the focus, and the estimated focus is determined. After moving the lens system or the color image sensor by the distance to the focal point in the direction of, it is determined again whether or not the lens is in focus, and if it is determined that the lens is in focus, the lens system is moved. Color correction by correcting chromatic aberration of subject light Since the image is formed on the child and normal photographing is performed, information on the distance and direction to the focal position can be obtained only by one imaging for AF, and high-speed focusing can be performed with a simple configuration. The operation can be performed.

According to the seventh aspect of the present invention, the object light is formed by the lens system without correcting the chromatic aberration, and each color of the image data in the AF area of the subject image formed on the color image pickup device. Calculate the point image distribution coefficients indicating the blur characteristics, calculate the point image radius of each color based on the calculated point image distribution coefficients of each color, and calculate the direction of the focal point and the focal point based on the calculated point image radius of each color. Is estimated based on the estimated distance to the focal point, and it is determined whether or not the subject is in focus. If it is determined that the subject is not in focus, the estimated direction of the focal point is determined. After moving the lens system or the color image sensor by the distance to the focal point, and moving the lens system or the color image sensor by the distance to the focal point in the direction of the estimated focal point, the focus state again. The camera is in focus, If it is determined that there is, the subject light is corrected for chromatic aberration by the lens system, and an image is formed on the color image pickup device, and normal photographing is performed. Information on the distance to the position and the direction can be obtained, and a high-speed focusing operation can be performed with a simple configuration.

According to the invention of claim 8, in the invention of claim 7, the image data in the AF area is multiplied by a window function and then two-dimensionally Fourier-transformed to be converted into amplitude and phase in the frequency domain. Then, after replacing each phase in the entire frequency domain with zero, two-dimensional inverse Fourier transform is performed to calculate the point spread coefficient. Therefore, in addition to the effect of the invention described in claim 7, DFT ( Discrete Fourier Transform) or FFT
(Fast Fourier Transform) and DSP (Digital Sig
It is suitable for digital integrated circuits such as nal processors.

According to a ninth aspect of the present invention, in the seventh or eighth aspect, the cross-sectional area is calculated based on the threshold value calculated based on the peak value of the point spread coefficient at the origin. Since the point image radius is calculated based on the calculated cross-sectional area, in addition to the effects of the invention according to claim 7 or claim 8, the point image cross-section is circular like an opening of a camera. Even in the case of a polygon that does not result in a circle, the point image radius in the case of circular approximation can be obtained, and the point image radius can be calculated easily and with high accuracy.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram for explaining the principle of the present invention.

FIG. 2 is an explanatory diagram for explaining an AF area of a color image sensor.

FIG. 3 is an explanatory diagram for explaining a method of determining the direction and distance of a focal point.

FIG. 4 is a diagram for explaining a relationship between a point image radius and a stop aperture diameter.

FIG. 5 is a configuration diagram of an AF processing system of the digital camera according to the first embodiment.

FIG. 6 is a flowchart illustrating an AF operation and a photographing operation of the digital camera in FIG. 5;

FIG. 7 is a flowchart for explaining in detail a point image radius calculation process in the flowchart of FIG. 6;

FIG. 8 is a flowchart for explaining in detail a focal length direction calculation process in the flowchart of FIG. 6;

FIG. 9 is an explanatory diagram for explaining a two-dimensional Hamming window function.

FIG. 10 is an explanatory diagram for explaining a point spread coefficient at the time of focusing.

FIG. 11 is an explanatory diagram for explaining a point spread coefficient at the time of out-of-focus.

FIG. 12 is an explanatory diagram for describing a method of calculating a point image radius.

FIG. 13 is an explanatory diagram for explaining a focal length L at the time of front focus.

FIG. 14 is an explanatory diagram for explaining a focal length L at the time of back focus.

FIG. 15 is a configuration diagram of an AF processing system of the digital camera according to the second embodiment.

FIG. 16 is a diagram illustrating an example of a lens arrangement in a case where a shooting and AF lens does not perform chromatic aberration correction.

17 is a diagram illustrating a relationship between a focal length and a color wavelength in the case of the lens arrangement in FIG. 16 (when chromatic aberration correction is not performed).

FIG. 18 is a diagram illustrating a lens arrangement in a case where a shooting and AF lens corrects chromatic aberration.

19 is a diagram illustrating a relationship between a focal length and a color wavelength in the case of the lens arrangement in FIG. 18 (when performing chromatic aberration correction).

[Explanation of symbols]

 Reference Signs List 101A AF lens 101B Shooting lens 101 Shooting and AF lens 102 Imaging aperture 103 Color image sensor 104 Automatic exposure control unit 105 AF area image data memory 106 Window function multiplication unit 107 Two-dimensional FFT unit 108 Phase operation unit 109 Two-dimensional IFFT Unit 110 Point image distribution coefficient memory 111 Distance direction calculation unit 112 Focus adjustment driving device 113 Photographing / AF switching device 114 Frame image memory 120 Point image distribution coefficient calculation unit

 ──────────────────────────────────────────────────続 き Continued on the front page F term (reference) 2H011 AA03 BA33 BB04 BB06 2H051 BA45 BA47 CB22 CE12 CE14 CE16 CE21 CE24 CE26 5C022 AA13 AB28 AB29 AB30 AB31 AB46 AC00 AC42 AC54 AC74 5C065 AA01 AA03 BB11 BB26 CC01 CCGG DD GG01

Claims (9)

[Claims] 1. An imaging system for forming an image without correcting chromatic aberration of subject light in imaging for AF, and a lens system for forming an image by correcting chromatic aberration of subject light in normal imaging, and an AF area in a central portion of the imaging area. A color imaging element configured to convert a subject image formed by the lens system into image data; and calculating blur characteristic information for each color of the image data in the AF area, based on the calculated blur characteristic information of each color. A focus position estimating means for estimating the direction of the focal point and a distance to the focal point; and determining whether or not the subject is in focus based on the focal point distance estimated by the focus position estimating means. Focusing state determining means, and when the focusing state determining means determines that the object is not in focus, the distance to the focusing point in the direction of the focusing point estimated by the focusing position estimating means, , The lens Or automatic focusing apparatus characterized by comprising a driving means for moving the color image sensor. 2. A first method for forming an image by correcting chromatic aberration of subject light.
And a chromatic aberration is generated on the optical axis so as to have different focal lengths for a plurality of visible light wavelengths, and a focal position of any one color in the visible light wavelength band is the same as the first lens. Lens switching means for switching to the first lens for normal imaging, and to the second lens for imaging for AF, and an AF area at the center of the imaging area Is set, and a color image sensor that converts a subject image formed by the first or second lens into image data; and a point image distribution coefficient indicating a blur characteristic for each color of the image data in the AF area. Focus position estimation for calculating the point image radius of each color based on the calculated point image distribution coefficient of each color, and estimating the direction of the focal point and the distance to the focal point based on the calculated point image radius of each color. Means, A focusing state determining unit that determines whether or not the camera is in focus based on the distance to the focal point estimated by the focusing position estimating unit; and a focusing state determining unit that determines that the camera is not in focus. A driving unit for moving the lens system or the color image sensor by a distance up to the focal point in the direction of the focal point determined by the focal position estimating unit when the determination is made. An automatic focusing device. 3. A lens group capable of switching between a first mode for forming an image by correcting chromatic aberration of the subject light and a second mode for forming an image without correcting the chromatic aberration of the subject light by a lens arrangement, and the lens. A lens switching unit that moves the lens group to switch the lens group to the first mode in normal imaging, and a lens switching unit to switch the lens group to the second mode in imaging for AF; An area is set, and a color image sensor for converting a subject image formed by the lens group into image data, and a point image distribution coefficient indicating a blur characteristic for each color of the image data of the AF area are calculated and calculated. A focus position estimating means for calculating a point image radius of each color based on a point image distribution coefficient of each color, and estimating a direction of a focal point and a distance to the focal point based on the calculated point image radius of each color; Focus A focus state determining unit that determines whether or not the camera is in focus based on the distance to the focal point estimated by the estimating unit; and a case where the focus state determining unit determines that the camera is not in focus. Driving means for moving the lens system or the color image sensor by a distance to the focus in the direction of the focus determined by the focus position estimating means. Focusing device. 4. The automatic focusing device according to claim 2, wherein the focus position estimating means multiplies the image data of the AF area by a window function, and performs a two-dimensional Fourier transform to perform frequency domain processing. An automatic focusing device, wherein the point image distribution coefficient is calculated by performing two-dimensional inverse Fourier transform after converting each phase of the entire frequency range to zero. 5. The automatic focusing device according to claim 2, wherein the in-focus position estimating unit calculates a threshold based on an origin peak value of the point image distribution coefficient. An automatic focusing device, wherein a cross-sectional area is calculated based on a value, and the point image radius is calculated based on the calculated cross-sectional area. 6. A focusing method of an automatic focusing device for performing an automatic focusing operation by moving a lens system or a color image pickup device, wherein the lens system forms an image of subject light without correcting chromatic aberration. Calculating the blur characteristic information for each color of the image data of the AF area of the subject image formed on the color image sensor, and based on the calculated blur characteristic information for each color, the direction of the focal point and the focal point. A second step of estimating a distance to the camera; a third step of determining whether or not the camera is in focus based on the estimated distance to the in-focus point; A fourth step of moving the lens system or the color imaging device in the direction of the estimated focal point by the distance to the focal point when it is determined that the lens is not in the state; Focus A fifth step of repeating the first to third steps after moving the lens system or the color image sensor by a distance to the focal point in a direction, and a third step. A sixth step of, when it is determined that the subject is in focus, correcting the chromatic aberration of the subject light by the lens system, forming an image on the color image sensor, and performing normal photographing; Focusing method for automatic focusing device. 7. A focusing method of an automatic focusing device for performing an automatic focusing operation by moving a lens system or a color image sensor, wherein the lens system forms an image of subject light without correcting chromatic aberration. And calculating a point spread coefficient indicating a blur characteristic for each color of the image data of the AF area of the subject image formed on the color image sensor, and calculating a point spread of each color based on the calculated point spread coefficient of each color. A second step of calculating an image radius and estimating a direction of a focal point and a distance to the focal point based on the calculated point image radius of each color; and focusing based on the estimated distance to the focal point. A third step of determining whether or not the camera is in a state; and, if it is determined in the third step that the camera is not in focus, the distance to the focus in the direction of the estimated focus. Only the lens system Moving the color image sensor, moving the lens system or the color image sensor in the direction of the estimated focal point by the distance to the focal point, A fifth step of repeating a step to a third step; and in the third step, when it is determined that the object is in focus, subject light is corrected for chromatic aberration by the lens system and the color image is captured on the color image sensor. 6. A focusing method for an automatic focusing device, comprising: a sixth step of forming an image and performing normal photographing. 8. The focusing method of the automatic focusing apparatus according to claim 7, wherein in the second step, after multiplying the image data of the AF area by a window function, the image data of the AF area is subjected to a two-dimensional Fourier transform to obtain a frequency domain. A focusing method for an automatic focusing device, comprising: converting into an amplitude and a phase; replacing each phase in the entire frequency range with zero; and performing a two-dimensional inverse Fourier transform to calculate the point spread coefficient. 9. The focusing method for an automatic focusing device according to claim 7, wherein the second step includes determining a threshold value calculated based on an origin peak value of the point spread coefficient. A focusing method for an automatic focusing device, wherein a cross-sectional area is calculated based on the calculated cross-sectional area, and the point image radius is calculated based on the calculated cross-sectional area.