RU2324914C2 - Method of identification of image areas distorted by comatic aberration, with subsequent correction - Google Patents

Abstract

FIELD: physics, instruments.

SUBSTANCE: substance of the method is as follows: the image transmitted by the optical system is used to determine the distance from an object point to the principal optical axis of the optical system; the diaphragm radius and the coordinates of the geometric centre of gravity of the point image, in the form of a light spot, are used to determine the diaphragm coordinates and the comatic aberration value, and identify distorted image areas. For the identification of distorted areas, points are searched, so that the brightness distribution function f(x, y) in a given figure would satisfy the value determined experimentally for the optical system when this figure is plotted from these points. The points found are grouped into arrays of points located in distorted areas, and the brightness of the points in the distorted areas is corrected by determining the true brightness of the distorted area points using the formula f_corr ⁼f_cur.-f(x,y), where f_cur. is the current brightness. The technical effect is the increase in the accuracy of the comatic aberration correction.

EFFECT: increase in accuracy of comatic aberration correction.

2 dwg

Description

The invention relates to computer technology and can be used both to find areas of the image distorted by comic aberration, and to correct comic aberration of the optical system of an optoelectronic sensor.

A known lens (RF patent No. 2258247, published August 10, 2005, according to application No. 2003107773/28 of March 17, 2003), in which the comatic aberration is corrected by a method that consists in the fact that the lens contains a positive component located on the side to correct aberration subject and including two lenses, one of which is biconvex, and a negative component located on the image side and made in the form of a meniscus.

The disadvantage is the presence after correction of residual aberrations caused by the introduction of additional lenses.

Closest to the proposed is a method of compensating for comatic aberration, (US patent No. 5726436, published March 10, 1998, according to the application No. 762508 of December 10, 1996), namely, that the objective lens collects a light beam of rays emitted by a light source located on an optical axis, the beam splitter separates the light beam emitted by the light source reflected by the light reflector from the optical disk, the detector detects the returned light separated from the light beam emitted by the light source. The first optical compensating device has a convex aspherical surface and is located on the optical path where the light beam is emitted by the light source. The second optical compensating device has a concave aspherical surface and is located on the optical path where the light beam is emitted by the light source.

The disadvantage of this method is the introduction of additional errors introduced for correction of compensating devices.

An object of the invention is to increase the accuracy of correction of comic aberration.

The problem is solved in that the image transmitted by the optical system determines the distance from the point of the object to the main optical axis of the optical system, the diaphragm coordinates are determined by the radius of the aperture and the coordinates of the geometric center of gravity of the image as a light spot, the magnitude of the com aberration is determined, the distorted areas are determined image, for which they search for points, when constructing from which a given figure, the brightness distribution function f (x, y) in this figure satisfies the value, e experimentally determined for the optical system, form arrays of points included in the distorted areas, correct the brightness of the points in the distorted areas by determining the true brightness of the points of the distorted area. The invention can be used to improve the accuracy of image transmission of optical systems during their operation.

The invention is illustrated by drawings, where Fig. 1 shows the path of rays during comatic aberration and indicates the points used in the calculations, Fig. 2 is a diagram used to determine areas distorted by comatic aberration.

Comatic aberration is one of the types of monochromatic aberration and consists in the fact that a beam that is symmetrical with respect to the main beam and enters the optical system becomes asymmetric upon exit from the system (Fig. 1) [Theory of optical systems. Textbook for high schools / B.N. Begunov, N.P. Zakaznov, S.I. Kiryushin, V.I. Kuzichev. - 2nd ed., Revised. and add. - M .: Mechanical Engineering, 1981. - P.158].

The presence of comatic aberration in the optical system leads to the fact that instead of the image in the form of a point, in the geometric sense of the word, there is a light spot that resembles a comet in its shape.

[Applied Optics. Apenko M.I., Dubovik A.S. M .: Nauka, Main edition of the physics and mathematics literature, 1971. - P.147].

Comatic aberration depends on the distance y from the point of the object to the main optical axis, the diaphragm coordinates m and M, constant for the optical system coefficient B.

Consider the determination of the distance y from the point of an object to the main optical axis.

Because the distance from the diaphragm to the main optical system with respect to the distance from the point of the object to the optical system is small, then it can be neglected. Thus, in order to find the distance from the point of the object to the main optical axis, the following calculations are performed:

r is the radius of the diaphragm;

f is the focal length;

r = ON = OK;

ST is the distance from the center of the image to the extreme point of the light spot.

Since the triangles of ATS and AOK are similar, then

From figure 1:

OC = f,

From triangle AOK

DT = | CT-r |,

ND = OS = f.

From the triangle DTN:

LH = y

Since the triangles LSH and SON are similar,

Let LO = l

From the OSN triangle:

From the ENK triangle:

EH = r-y,

Let n be the refractive index, defined as follows:

sin φ = n

sin γ = n

tgγ = tg (arcsin (sin γ)) = tg (arcsin (n · sin γ ')),

tgφ = tg (arcsin (sin φ)) = tg (arcsin (n · sin φ ')),

tgγ = tg (arcsin (n * sin (arctan (tgγ ')))),

tgφ = tg (arcsin (n * sin (arctan (tgφ ')))),

From the formula (*) it follows:

l = tgφ (r + y)

From the formulas (*) and (**) it follows:

at γ> 90 °:

tgγ · tgφ · (r + y) = r-y,

tgγ · tgφ · r + tgγ · tgφ · y = r-y,

r · (1-tgγ · tgφ) = y · (1 + tgγ · tgφ),

at γ <90 °:

tgγ · (r-y) = tgφ · (r + y),

tgγ · r-tgγ · y = tgφ · r + tgφ · y,

r · (tgγ-tgφ) = y · (tgγ + tgφ),

In this way,

Aperture coordinates are determined by the image with a known aperture radius by determining the polar coordinates (r, a), where a is the angle determined by the coordinates of the geometric center of gravity of the light spot image, r is the radius of the aperture, and the subsequent transition to Cartesian coordinates (m, M) .

After finding the distance from the point of the object to the optical axis y and the aperture coordinates m and M, the amount of comatic aberration is found by the formula

Δy '= By (3m ² + M ² ),

where Дy 'is the value of comatic aberration.

To correct comic aberration, distorted areas are detected. For this, from the extreme point T of the light spot (Fig. 2), a distance equal to the amount of comatic aberration is laid aside. Then, from the obtained point P, two auxiliary lines are constructed at an angle of 30 degrees to the line PT (Fig. 2). Next, build a circle of radius RT.

To identify a distorted area that needs correction, it is necessary to know the coordinates of the points P, U, V, R. For this, with the known coordinates of the point T, the following calculations are performed. Consider the calculations for the first quarter of the image (for x> 0, y> 0). For the remaining quarters, the calculations will be similar.

Let (x _T , y _T ) be the coordinates of the point T (Fig. 2).

Because C is the center of the image, taken as the origin,

CT _Y = TT _x = y _T , CT _X = x _T.

From figure 2 it is seen that the angle TCT _x is equal to the angle TPJ, therefore:

tg∠TCT _x = tg∠TPJ,

It is known that RT (figure 2) is the amount of comatic aberration equal to Dy '

Consider the PTJ triangle:

By the Pythagorean theorem:

From formulas (1) and (2):

From formulas (2) and (3):

Let (x _P , y _P ) be the coordinates of the point P (Fig. 2).

x _P = x _T -PJ,

y _P = y _T -TJ.

Consider equal triangles UPR and VPR:

Because angle UPJ = 60 ° [Applied optics. Apenko M.I., Dubovik A.S. M .: Nauka, General Physics and Mathematics, 1971. - P.147], the angles of UPR and VPR are 30 °,

sin∠UPR = sin∠VPR,

PR = 2UR.

Because UR = VR = RT (Fig. 2)

Δy '= PT = PR + RT = 2UR + RT = 2RT + RT = 3RT,

Let (x _R , y _R ) be the coordinates of the point R (Fig. 2). These coordinates are determined similarly to the coordinates of point P (formulas (5) and (6)).

Because

Angle

By the Pythagorean theorem:

From the triangle PUU _x .

y _U = y _P + UU _x ,

Angle

The coordinates of the point V are found similarly to the coordinates of the point U. Thus, according to formulas (11) and (12):

The result is an area bounded by two straight lines and an arc of a circle centered at point R. This area needs correction.

To determine all distorted areas of the image, a search is made for the points in sequence, when constructing from which a given figure, the law of brightness distribution satisfies the template value predefined for each specific optical system, after which, when this condition is fulfilled, an array of points is included in the distorted area for correction.

The brightness of the points in the distorted areas is corrected by determining the true brightness of the points of the distorted area. The brightness is determined by the formula

f _cor = f _tech -f (x, y),

where f _tech is the current brightness, f (x, y) is the brightness distribution function in the distorted region depending on the distance from the extreme point of the light spot, determined experimentally for each optical system.

The method allows to improve the quality of images by improving the accuracy of correction of comic aberration by finding areas of the image distorted by comatic aberration and their subsequent correction.

Claims (1)

The method of finding image areas distorted by comatic aberration, which consists in determining the distance from the point of the object to the main optical axis of the optical system using the image transmitted by the optical system, and the diaphragm coordinates are determined by the radius of the aperture and the coordinates of the geometric center of gravity of the image of the point in the form of a light spot find the amount of comatic aberration, determine the distorted areas of the image, for which they search for points, when building from which the given fig In this figure, the brightness distribution function f (x, y) satisfies the value experimentally determined for the optical system, form arrays of points included in the distorted areas, and correct the brightness of the points in the distorted areas by determining the true brightness of the points of the distorted area using the formula f _box = f _tech. -f (x, y) where f _tech. - current brightness.

Images