DE2728304C2 - Light beam scanning device - uses vibrating mirror and focussing lens to move light spot at uniform velocity over surface - Google Patents

Abstract

A drive for the deflecting mirror vibrates it so that its rotational angle phi is equal to phi 0 sin K1t. There is a light source for generating an afocal beam toward the deflecting mirror. There is a focussing lens disposed between the deflecting mirror and a surface to be scanned as having an optical axis passing through the centre of the deflecting mirror, for imaging the beam on the surface to be scanned in a form of a spot. The focussing lens has a distortion characteristic represented by a given mathematical formula.

Description

The invention relates to an optical-mechanical scanning system according to the preamble of patent claim 1.

An optical-mechanical scanning system according to the preamble of claim 1 is known. In this scanning system, the scanning mirror is moved at a uniform angular velocity, with the aid of a downstream lens ensuring that the scanning point moves as uniformly as possible on the scanning plane. - Since galvanometer mirrors are typically used as scanning mirrors, a current must be supplied to the coil of the galvanometer mirror in such a way that a uniform angular velocity is obtained. However, it is difficult to generate such a carrier current, particularly if a high scanning frequency is desired.

The invention is based on the object of developing an optical-mechanical scanning system in such a way that a uniform movement of the scanning point on the scanning plane is achieved even with an easily generated oscillation characteristic of the scanning mirror.

This object is achieved according to the invention by the features specified in the characterizing part of patent claim 1. By using a sinusoidally oscillating mirror, it is easily possible to drive it even at high frequency. The non-uniformity of the movement of the scanning point that would otherwise arise from the use of a sinusoidally oscillating mirror is compensated by a suitable distortion characteristic of the imaging lens system.

Embodiments of the invention are specified in the subclaims.

The invention is described in more detail below using exemplary embodiments with reference to the drawing. It shows

Fig. 1 schematically shows the optical arrangement in a first embodiment of the optical scanning system.

Fig. 2 shows schematically the optical arrangement in a second embodiment in which a light source is located at infinity.

Fig. 3 is a sectional view of a lens system having a distortion characteristic according to an equation (12) shown below.

Fig. 4 and 5 Values of the deviation of the focusing position from an ideal image height of lens systems according to Tables 1 and 2 below.

Fig. 6 schematically shows an embodiment of a data processing terminal unit in which the optical-mechanical scanning system is used.

Fig. 7 graphically shows the relationship between the amplitude large Phi[low]0 of an oscillating mirror and the distortion coefficient V of third order.

Fig. 8 schematically shows the refractive power distribution of a lens system used in the scanning system for scanning.

Fig. 9 graphically shows the changes in the Petzval sum caused when the refractive power arrangement of the lens system according to Fig. 8 is varied.

Fig. 10 to 36 graphically show the changes of specific coefficients B[deep]01 and B[deep]02 for various embodiments of the lens system of the data processing terminal unit according to Fig. 6.

Fig. 37 Types of scanning lens systems usable in the data processing terminal unit.

Fig. 38, 39 (A), 40 to 44, 45 (A), 46 to 56, 57 (A), 58 to 61, 62 (A), 63 and 64 show different embodiments of the lens system for scanning which can be used for the data processing terminal unit.

Fig. 39 (B) Image aberrations of the lens system according to Fig. 39 (A).

Fig. 45 (B) Image aberrations of the lens system according to Fig. 45 (A).

Fig. 57 (B) Image aberrations of the lens system according to Fig. 57 (A).

Fig. 62 (B) Image aberrations of the lens system according to Fig. 62 (A).

Fig. 65 and 66 schematically show applications of the optical scanning system to data processing terminal units.

Fig. 1 shows the arrangement of an embodiment of the optical-mechanical scanning system with a light source S which is at a distance r from the center O of a sinusoidally oscillating mirror M. i denotes a light beam directed by the light source S onto the center O of the mirror M, i' denotes a light beam reflected by the mirror M, L denotes a lens, g the optical axis of the lens and P' the image plane of the lens L. Large Phi is the angle of rotation by which the mirror M is rotated in relation to its reference position as shown by the dashed line, at which the light beam i' coincides with the optical axis of the lens L. The angle of rotation large Phi is related to the time t as follows:

large Phi = large Phi[deep]0 times sin k[deep]1 times t

(1)

The following applies:

k[deep]1 = time constant

large Phi[low]0 = amplitude of the torsional oscillation

Let small Omega' be the angular velocity (d large Phi/d t) of the mirror. Using equation (1), small Omega' can be expressed as:

(2)

If the distance between the center O of the mirror M and the principal point N of the lens L at its entrance side is l, the light ray i can be considered as if it were reflected from the mirror, and the reflected light ray i' can be considered as if it came from a point S' on an arc P whose center of curvature is the center O of the mirror. Suppose that large theta is the angle between the straight line through the point S' to the principal point N of the lens L at its entrance side and the optical axis g. The following relationship exists between large theta and large phi:

tan big theta = rsin 2 big phi/(l + rcos 2 big phi)

(3)

By differentiating both sides of equation (3) with respect to time t, the following equation is obtained for small values of the angle large theta:

From this we get equation (2):

(4)

On the other hand, if it is required that the absolute value of the scanning speed of an image point y' on the image plane P' of the lens L is constant, then

(5)

with k[deep]2 = constant.

From equations (3), (4) and (5) the following equations can be derived:

(6)

(6)'

where the mapping function F(large theta) is given by:

(7)

and the only angle-dependent function f(large theta) by:

(8th)

From equation (6)' the following applies for the image point y':

(9)

The integration constant is omitted from the above equation, since it is 0 if it is assumed that at large theta = 0 the image point or the image height y' = 0. For small angles large theta, i.e. for the paraxial area, cos large theta is approximately equal to 1 and sin large theta approximately equal to 0, so that: f (large theta) = r and large phi = 0. With these values, F (large theta) = (l+r)/(r large phi[low]0) and thus

On the other hand, in the paraxial region, the following applies to the image location y' with f[deep]infinity as the paraxial focal length:

y' = f[deep]infinity times large theta

so that from these two relations the value of the constant k[deep]2 in the paraxial region follows:

(10)

Strictly speaking, this value of the constant k[deep]2 is only valid for small angles, large theta and large phi, i.e. only for the paraxial range. From equations (5) and (10) it can be seen that the scanning speed on the focusing surface has a constant value if the lens L is designed in such a way that its specific distortion characteristics satisfy the conditions of equations (7), (8) and (9).

In the first embodiment shown in Fig. 1, it was assumed that the light source S is located at a finite distance r; in the second embodiment shown in Fig. 2, however, the light source S is optically at infinity.

In this case, 2 large Phi = large Theta and equations (1) and (2) become:

Furthermore, if in equation (6) large Phi = large Theta/2 and r = infinity, the following equation is obtained:

thats why

(11)

If we take into account in equations (10) and (11) that r = infinity, we obtain:

(12)

This means that if the light source is optically at infinity, namely a parallel beam is scanned or deflected by means of the sine-wave mirror, and a lens with a distortion characteristic according to the expression y' = 2 large Phi[deep]0 f[deep]infinite arcsin (large theta/2large Phi[deep]0) is used, a scanning with a uniform speed can be achieved on the focusing surface.

Equation (12) is rewritten as follows:

y' = F times arcsin small delta

(13)

F = k times f infinity (k congruent 2 large Phi[deep]0 f infinity : focal length)

(14)

The image height y' at which a light beam is focused by means of a lens can be represented as a function of the angle (of incidence) large theta of the light beam on the lens, namely as a series expansion

(15)

with A[deep]1 as development coefficient, where the focal length is "1".

With V as the third order Seidel distortion coefficient, the relationship between this coefficient and the distortion can be expressed by the following equation (again for the focal length "1"):

(16)

From equations (15) and (16) it follows that with tan large theta is approximately equal to large theta + 1/3 large theta[to the power]3 and neglecting the expressions of fourth and higher order:

(17)

Equation (17) is satisfied for any value of large theta by:

A[deep]0 = A[deep]2 = 0

A[deep]1 - 1 = 0

(18)

Using equations (15) and (18), the image height y' in the range of the third order aberration can therefore be expressed as:

y' = big theta + A[low]3 big theta[high]3

With a focal length other than "1" this results in:

y' = f(big theta + A[low]3 big theta[high]3)

(19)

The third order distortion coefficient V is given by equation (18):

(20)

From equations (19) and (20) it is possible to determine a lens system that satisfies equation (12), so that consequently the third order distortion coefficient V is equal to

(21)

is.

For the fifth order distortion coefficient V we get in a similar way:

(22)

For simplicity, assume that k=1. If the following values are assumed: Thus, the light deflected by the sinusoidally oscillating mirror can be made to scan the scanning surface at a uniform speed.

Fig. 7 shows the change in the third order distortion coefficient resulting from a change in the amplitude of large Phi[low]0. As can be seen from Fig. 7, the value of V becomes negative and smaller the smaller the amplitude of large Phi[low]0 is.

For ordinary lenses, the Seidel aberration coefficients to be corrected in conjunction with the third-order distortion coefficient are:

I = spherical aberration,

II = coma,

III = astigmatism,

P = Petzval sum.

For a focal length of f = 300 mm, an aperture number F[deep]N0 = 60 and a half angle of view small omega/2 = 20°, the still acceptable ranges of I and II are calculated under the assumption that the spot size on the focal plane approaches the diffraction limit. At F[deep]N0 = 60, the spot size for light of wavelength small lambda = 0.6328 µm is approximately 0.1 mm, so that if the halo and coma in the focal plane are 0.05 mm or less and the consideration is limited to third-order aberration coefficients, the following applies, without this being demonstrated in detail here:

(23)

(24)

where small alpha'k is the angle of inclination of the paraxial ray on the image side, which can be represented by 1/f, and R is the radius of the entrance pupil when the focal length of the entire system is normalized to "1".

Therefore, |I| is less than or equal to 57.6 and |II| is less than or equal to 4.4.

It follows that little attention should be paid to the correction of spherical aberration and coma, but in view of the wide angle of view, astigmatism III, Petzval sum P and distortion V are the aberrations that must be corrected. Of these three aberrations, P can be taken into account when determining the refractive power distribution of the lens system.

It can be seen from this that the aberrations in the scanning system of the type described which have to be taken into account are only astigmatism III and distortion V in the range of the third order coefficients.

An embodiment of the scanning optical system used in a data processing terminal unit will be described below. Fig. 6 shows a modulation light source 1 such as a semiconductor laser which emits a light signal having a modulated light intensity, a condenser lens 2, a slit 3 arranged at a location where the light from the modulation light source is collected by the condenser lens 2, and a collimator lens 4 arranged so that its front focal point coincides with the slit 3. In this way, the light transmitted through the slit 3 passes through the collimator lens 4 and is collimated by it into a parallel light beam. The parallel light beam from the collimator lens 4 is reflected by the reflecting surface of a mirror 5 of a galvanometer mirror array, and the reflected light in the form of a parallel beam enters and passes through a lens system 6 so as to be focused on a scanning surface (sensitive film) 7. To achieve rapid oscillation of the mirror 5, a high frequency current must be supplied to the coil of the galvanometer mirror assembly. Therefore, by supplying a high frequency current in sinusoidal form to the coil, the mirror is set into a sinusoidal oscillation at high speed. If the lens system 6 used were a "y' = f tan large theta" lens, whose image height is proportional to the tangent of the deflection angle large theta, or a "y' = f large theta" lens, whose image height is proportional to the deflection angle large theta, the movement of the light spot on the scanning surface would not be at a constant speed.

For this reason, in the data processing terminal unit shown in Fig. 6, the scanning system operates with a lens system whose image height y' satisfies equation (12) and which has a large image angle.

In the following, two embodiments of a lens system are explained which have a lens structure according to Fig. 3. In Fig. 3 and in the following Tables 1 and 2, the following mean:

r[deep]1 = radius of curvature of the i-th lens surface

d[deep]1 = air gap or lens thickness on the optical axis

n[deep]1 = refractive index of the i-th element

v[deep]1 = Abbe number of the i-th element

small lambda = light wavelength

Lens example 1 (Table 1)

With the focal length f = 120.90236, the aperture number F[deep]NO = 60 and the half angle of view small Omega/2 = 23.1°, the lens has a focusing performance that essentially reaches the diffraction limit, and the deviation of the actual image height y' from the ideal image height according to equation (13) at the maximum image height of 50 mm is approximately -0.16 mm as shown in Fig. 4. In this case, the distortion coefficients are third and fifth order (see Table 3)

V = 0.35410 so that the third-order distortion coefficient is essentially close to the target value, but the fifth-order distortion coefficient is still insufficient (compared to the values of V and according to equation (22) for k = 1).

Table 1

Lens example 2 (Table 2)

With the focal length f = 120.90236, the aperture number F[deep]NO = 60 and the half angle of small Omega/2 = 28.6°, the lens has a focusing performance that essentially reaches the diffraction limit, and the deviation of the actual image height y' from the ideal image height according to equation (13) at the maximum image height of 63 mm is approximately -0.15 mm as shown in Fig. 5. In this case, the third and fifth order distortion coefficients are

V = 0.35603 therefore, both the third-order distortion coefficient and the fifth-order distortion coefficient substantially satisfy their target values, resulting in that the lens system of Example 2 is improved in performance up to a large angle of view compared with the lens system of Example 1.

Table 2

Table 3

In Table 3, the aberration coefficients I, II, III, P and V have the meaning already explained above. The following applies to the fifth order aberration coefficients:

The lens system of the scanning system preferably has two subsystems which are spaced apart from each other by a finite distance, each of these subsystems being a single lens or a two-part lens. Such a lens system can be divided into three types depending on the refractive power arrangement of each subsystem. The first type is the case where the first subsystem arranged towards the deflection device, i.e. the mirror, has negative refractive power and the second subsystem arranged towards the scanned surface has positive refractive power. The second type is the case where the first subsystem directed towards the deflection device has positive refractive power and the second subsystem arranged towards the scanned surface has negative refractive power. It is assumed that large Psi[deep]1 is the refractive power of the first subsystem, large Psi[deep]2 is the refractive power of the second subsystem and B[deep]01 is a specific coefficient of the first subsystem, which will be described below. Under the conditions that the focal length of the lens system is "1" and the refractive indices n[deep]1 and n[deep]2 of the first and second subsystems are 1.46 less than or equal to n[deep]1 less than or equal to 1.84 and 1.46 less than or equal to n[deep]2 less than or equal to 1.84, the values large Psi[deep]1, large Psi[deep]2 and B[deep]01 in the lens system of the first type should satisfy the following conditions:

-5.5 less than or equal to large Phi[deep]1 less than or equal to -0.35

1.2 less than or equal to large Phi[deep]2 less than or equal to 5.7

-10 less than or equal to B[deep]01 less than or equal to 3

and for the lens system of the second type, the following conditions must be met:

1.35 less than or equal to large Phi[deep]1 less than or equal to 5.5

-5.3 less than or equal to large Phi[deep]2 less than or equal to -0.4

-13 less than or equal to B[deep]01 less than or equal to 4

If the light beam guided through the lens system does not consist of monochromatic light, for example light of a plurality of wavelengths or white light, a two-part lens can be used for each of the subsystems, so that in such cases a color error can be easily corrected.

According to the aberration theory, it is clear that the degree of freedom for aberrations that can be changed by changing the shape of the lens surfaces of only a thin single lens is equal to "1".

The aberrations in the lens system of the types explained here that must be taken into account are astigmatism III and distortion V, so that if the lens system has two subsystems to correct these two aberrations and each of these subsystems is a single lens, the degree of freedom for the aberrations is equal to "2" and thus a solution exists that enables the aberrations in the lens system of this type to be adjusted to the nominal values of the aberration coefficients.

The above is explained using mathematical expressions. According to equation (21) it is required:

Furthermore, the following condition is specified:

III = 0 .

This determines the target values of V and III.

Furthermore, it is specified that the lens system has two subsystems, each of which is a thin single lens. With these specifications, the shape of the thin single lens in each subsystem is to be determined, taking into account the refractive power distribution of the two subsystems.

The third-order aberration coefficients of a lens system consisting of two subsystems are the sum of the corresponding aberration coefficients of the subsystems. The third-order aberration coefficients of the lens system are therefore given by equation (4.37) on page 126 of the book "How to Design Lenses" by Joshiya Matsui, 1972, Ryoritsu Shuppan Co. Ltd., assuming that the focal length of the lens system is "1".

(25)

(26)

(27)

(28)

(29)

The index "1" applies to the first subsystem and the index "2" to the second subsystem. The total refractive power (large Psi) of the lens system is as follows:

big Psi = big Psi[deep]1 + big Psi[deep]2 - e' big Psi[deep]1 big Psi[deep]2

(30)

where e' is the distance between the principal points of the first and the second subsystem (see M. Born and E. Wolf "Principles of Optics" Pergamon Press, Third Edition, page 162, equation (26)).

In the above equations (9) to (13), the coefficients a[deep]1 to c[deep]V are defined by equation (4.38) on page 127 of the above-mentioned publication "How to Design Lenses". The following definitions apply to the specific coefficients or eigencoefficients A[deep]01, B[deep]01 and P[deep]01 (A[deep]01 is not identical to the coefficients used in equations (1) to (6)
<Unreadable>

(31)

(32)

(33)

where the index i again applies to the first or second subsystem and accordingly becomes "1" or "2" and where r is the radius of curvature of the front lens surface of the thin single lens forming the respective subsystem. The above-mentioned equations (31), (32) and (33) result from equation (4.29) on page 116 of the above-mentioned publication "How to Design Lenses" from the already mentioned

Assuming that the focal length is "1" and thus the total refractive power of the lens system is also "1", which means that in the equation (4.29) mentioned above, large Psi[deep]1 is to be set to 1. Furthermore, small Alpha[deep]1 is to be set to 0.

From equations (31) and (32), A[deep]0 can be expressed by B[deep]0 as follows:

(34)

(35)

Inserting equation (34) into equations (27) gives:

(36)

Inserting equation (34) into equation (28) and equating it with equation (21) gives:

(37)

Eliminating B[low]02[high]2 from equations (36) and (37) to express B[low]02 by B[low]01 gives:

(38)

(39)

Inserting equation (38) into equation (36) and eliminating B[deep]02, taking into account the specification III = 0, results in:

(40)

In this way, by solving the fourth order equation (40), the value of the coefficient B[deep]01 of the first subsystem is obtained, in which the aberration coefficients III and V of the third order of the lens system By inserting B[deep]01 into equation (38), the value B[deep]02 of the second subsystem is obtained. Once B[deep]01 and B[deep]02 are obtained in this way, the shapes of the first and second subsystems can be determined by equation (32).

As mentioned above, there are three types of focusing lens systems consisting of two subsystems, namely, positive lens/positive lens, positive lens/negative lens and negative lens/positive lens, viewed from the deflector side or the mirror. However, in the positive/positive lens type, the two subsystems have positive refractive power, so that the Petzval sum is larger. Therefore, the curvature of the image field and the astigmatism cannot be corrected. Regarding the positive/negative lens type and the negative/positive lens type, the respective suitability is determined by the amplitude of the oscillating mirror. The reason for this is that the required value of the distortion coefficient V is changed by the amplitude large Phi[low]0, as can be seen from equation (21). As can be seen from Fig. 7 and equation (21), the distortion coefficient V approaches the value 2/3 for increasing amplitude, is "0" for large Phi[deep]0 = 20.2571° and becomes negative and increasingly smaller with smaller large Phi[deep]0. Therefore, when the amplitude is large, the distortion required in the lens system is negative, at the amplitude large Phi[deep]0 = 20.2571° it is equal to "0" and at small amplitude large Phi[deep]0 it is positive. Therefore, when large Phi[deep]0 is large, it is necessary to arrange a positive lens at a larger chief ray height to form negative distortion, while when the amplitude large Phi[deep]0 is small, it is necessary to arrange a negative lens at a larger chief ray height to form positive distortion. In the lens system of this type, the entrance pupil of the same is located in front of it and the larger chief ray height necessarily gives the rear subsystem. Accordingly, as a two-part lens system, the negative/positive lens type is suitable for a large amplitude (large Phi[deep]0), the negative/positive or the positive/negative lens type is suitable for an amplitude of large Phi[deep]0 = 20° or close to 20°, and the positive/negative lens type is suitable for a small amplitude (large Phi[deep]0).

In Fig. 8, which shows the refractive power arrangement or distribution of the lens system, 8 denotes a deflecting surface which is an entrance pupil as seen from the lens system, t[deep]1 is the distance from the entrance pupil to the principal point of the first subsystem of the lens system, and e' is the distance between the principal points of the first and second subsystems. If large Psi[deep]1 is changed while setting t[deep]1 and e', large Psi[deep]2 is also changed according to equation (30). At the same time, according to equation (29), the Petzval sum P is changed as shown in Fig. 9. (Note that t[deep]1 is not shown since it has no relation to P. n[deep]1 and n[deep]2 are assumed to be typically n[deep]2 = n[deep]2 = 1.65.) Figs. 10 to 36 show changes in B[deep]01 and B[deep]02 resulting from changing the refractive power arrangement according to the tolerance of when the focal length of the entire system is "1", and by solving the fourth order equation (40) with respect to each power arrangement, where the nominal values III = 0 and V = 2/3 (1-1/2 k[high]2). Figs. 10 to 18 concern the amplitude large Phi[low]0 = 20° (nominal value V = -0.01725): Fig. 10 shows the changes in B[low]01 and B[low]02 obtained by changing large Psi[low]1 at e' = 0.015 and t[low]1 = 0.05,

Fig. 11 shows those at e' = 0.015 and t[deep]1 = 0.25,

Fig. 12 shows those at e' = 0.015 and t[deep]1 = 0.4,

Fig. 13 shows those at e' = 0.1 and t[deep]1 = 0.05,

Fig. 14 shows those at e' = 0.1 and t[deep]1 = 0.25,

Fig. 15 shows those at e' = 0.1 and t[deep]1 = 0.4,

Fig. 16 shows those at e' = 0.2 and t[deep]1 = 0.05,

Fig. 17 shows those at e' = 0.2 and t[deep]1 = 0.25,

Fig. 18 shows those at e' = 0.2 and t[deep]1 = 0.4.

Fig. 19 to 27 concern the amplitude of large Phi[low]0 = 15° (setpoint V = -0.5492): Fig. 19 shows the amplitudes achieved by changing large Psi[low]1.

Changes of B[deep]01 and B[deep]02; at e' = 0.015 and t[deep]1 = 0.05,

Fig. 20 shows those at e' = 0.015 and t[deep]1 = 0.25, Fig. 21 shows those at e' = 0.015 and t[deep]1 = 0.4

Fig. 22 shows those at e' = 0.1 and t[deep]1 = 0.05,

Fig. 23 shows those at e' = 0.1 and t[deep]1 = 0.25,

Fig. 24 shows those at e' = 0.1 and t[deep]1 = 0.4,

Fig. 25 shows those at e' = 0.2 and t[deep]1 = 0.05,

Fig. 26 shows those at e' = 0.2 and t[tief]1 = 0.25 and

Fig. 27 shows those at e' = 0.2 and t[deep]1 = 0.4.

Fig. 28 to 36 concern the amplitude of large Phi[deep]0 = 10° (setpoint V = -2.069): Fig. 28 shows the changes of B[deep]01 and B[deep]02 obtained by changing large Psi[deep]1 at e' = 0.015 and t[deep]1 = 0.05,

Fig. 29 shows those at e' = 0.015 and t[deep]1 = 0.25,

Fig. 30 shows those at e' = 0.015 and t[deep]1 = 0.4,

Fig. 31 shows those at e' = 0.1 and t[deep]1 = 0.05,

Fig. 32 shows those at e' = 0.1 and t[deep]1 = 0.25,

Fig. 33 shows those at e' = 0.1 and t[deep]1 = 0.4,

Fig. 34 shows those at e' = 0.2 and t[deep]1 = 0.05,

Fig. 35 shows those at e' = 0.2 and t[deep]1 = 0.25 and

Fig. 36 shows those at e' = 0.2 and t[deep]1 = 0.4.

In Figs. 10 to 36, six types of lens system with two subsystems, each of which is a thin single lens, are distinguished, namely types A, B, C, D, E and F according to Fig. 37, of which types A and B belong to the first type (negative/positive) and types C, D and E to the second type (positive/negative).

For type A, the value of |B[deep]0| is larger than for type B, ie, as can be seen from equation (32), the curvature is
<Unreadable>
larger, so that higher order aberrations are difficult to correct. Similarly, in the positive/negative lens type C, the value of |B[deep]0| is larger than that of the other types D, E and F, so that higher order aberrations are difficult to correct. In the negative/positive lens type, type B has a relatively small value of |B[deep]0|, while in the positive/negative lens type, the three types D, E and F have a relatively small value of |B[deep]0|, so that these types are suitable for practical use in that even if the thickness of the lens system is increased, a wide angle of view can be ensured without generating higher order aberrations.

The ranges of large Psi[deep]1, large Psi[deep]2 and B[deep]01 given for the lens systems of the first and second type are established for the following reasons:

If the upper limits of large Psi[low]1 and large Psi[low]2 are exceeded, the refractive power of the first subsystem must be made large to achieve large higher order astigmatism contributions, which in turn burdens the field of view performance.

If the lower limits of large Psi[deep]1 and large Psi[deep]2 are exceeded for types B, D and F, the curvature of the first subsystem of the lens system must be made larger in order to achieve higher order aberration contributions, which in turn affects the angle of view properties.

If the lower limits of large Psi[deep]1 and large Psi[deep]2 are exceeded for type E, there is no design for this type that simultaneously satisfies the requirements of III and V.

If the upper limits of large Psi[deep]1 and large Psi[deep]2 are exceeded in type B, there is no concave-convex formation that simultaneously fulfills the conditions for III and V.

If the upper limits of large Psi[deep]1 and large Psi[deep]2 are exceeded for types D and F, there is no design for these types that simultaneously satisfies the conditions for II and V.

If the upper limits of large Psi[deep]1 and large Psi[deep]2 are exceeded for type F, the curvature of the first subsystem must be increased to achieve higher order aberration contributions, which in turn affects the angle of view properties.

The distance e' between the principal points of the first and second subsystems is determined from equation (30) by inserting large Psi[deep]1 and large Psi[deep]2 within the tolerance of P.

The size t[deep]1 has no relation to the Petzval sum. Regarding the dimensioning of t[deep]1, it should be noted that the outer diameter of the lenses is larger when t[deep]1 is larger, and that the lens system hits the deflection device when t[deep]1 is too small.

The following are data of lens systems for scanning that can be used in the data processing terminal unit shown in Fig. 6.

Embodiments 3 to 6 are lens systems belonging to the above-described type B; the shapes of the lenses corresponding to these embodiments are shown in Figs. 38 to 41. Embodiments 7 to 15 are lens systems belonging to the above-described type D; the shapes of the lenses corresponding to these embodiments are shown in Figs. 42 to 50. Embodiments 16 to 22 are lens systems belonging to the above-described type E; the shapes of the lenses corresponding to these embodiments are shown in Figs. 51 to 57. Embodiments 23 to 29 are lens systems belonging to the above-described type F; the shapes of the lenses corresponding to these embodiments are shown in Figs. 58 to 64. A graphical representation of the aberrations is shown for one embodiment of each type, namely for the fourth embodiment according to type B, for the tenth embodiment according to type D, for the 22nd embodiment according to type E and for the 27th embodiment according to type F.

In the lens data listed below, r represents the radius of curvature of the respective lens surface, d represents the axial air gap or the axial thickness of each lens. d[deep]0 is the distance between the deflecting surface (entrance pupil) and the lens surface r[deep]1. n represents the refractive index of each lens, f the total focal length of the lens system, F[deep]NO its f-number and small omega/2 half the angle of view of the lens system. E represents the scanning power and is defined by (small omega/2)/2 large phi[deep]0. As already mentioned, large phi[deep]0 is the amplitude of the deflection device, i.e. the oscillating mirror, and the nominal value of the distortion coefficient V is determined by equation (21) and is given in parentheses in the line next to large phi[deep]0.

In any graphical representation of aberrations, SA represents the spherical aberration, AS represents the astigmatism, and the linearity is defined by where y' is the actual image height of the chief ray guided through the lens system and its deviation from the ideal image height according to equation (12) expressed as linearity.

Type B

3. Example (Fig. 38)

4. Example

(Fig. 39 A, aberrations in Fig. 39 B)

5. Example (Fig. 40)

6. Example (Fig. 41)

Type D

7. Example (Fig. 42)

8. Example (Fig. 43)

9. Example (Fig. 44)

10. Example

(Fig. 45 A, aberrations in Fig. 45 B)

11. Example (Fig. 46)

12. Example (Fig. 47)

13. Example (Fig. 48)

14. Example (Fig. 49)

15. Example (Fig. 50)

Type E

16. Example (Fig. 51)

17. Example (Fig. 52)

18. Example (Fig. 53)

19. Example (Fig. 54)

20. Example (Fig. 55)

21. Example (Fig. 56)

22. Example (Fig. 57 A, aberrations in Fig. 57 B)

23. Example (Fig. 58)

24. Example (Fig. 59)

25. Example (Fig. 60)

26. Example (Fig. 61)

27. Example

(Fig. 62 A, aberrations in Fig. 62 B)

28. Example (Fig. 63)

29. Example (Fig. 64)

Fig. 65 is a perspective view of a laser beam printer to which the optical scanning system is applied. In Fig. 65, a laser beam generated by a laser oscillator 11 is directed to the entrance port of a modulator 13 via a mirror 12. The beam modulated in the modulator 13 with information signals to be recorded is expanded in diameter by a beam expander 14, remaining a parallel beam, and then impinges on a mirror 15 which oscillates in a sinusoidal shape. The beam deflected by the oscillating mirror 15 is focused on a photosensitive drum 17 by a lens system 16 serving as a focusing lens. The beam deflected by the mirror 15 therefore sweeps over the photosensitive drum 17 at a uniform speed. 18 and 19 denote a first corona charger and an AC corona discharger, respectively, both of which form part of the electrophotographic process.

Fig. 66 shows an example of a reading apparatus to which the scanning optical system is applied. The reading apparatus is of a type in which a light beam from a conventional external illumination source (not shown) is read when it is reflected by a scanned surface. 21 denotes the scanned surface, 22 denotes a lens system serving as a focusing lens, such as one of the above-described type having a negative lens 22a on the deflector side and a positive lens 22b on the scanning surface side. 23 denotes a sinusoidally vibrated mirror as a deflector, 24 denotes a condenser lens, 25 denotes a slit plate having a slit 25a, and 26 denotes a photoelectric conversion element. In this way, the beam from the scanned surface 21 is guided over the lens system 22 and deflected by the deflection device, after which the beam is focused on the slit plate 25 by the condenser lens 24 and is detected via the slit 25a by the photoelectric conversion element 26. The points to be read on the scanning surface 21 are scanned at a uniform speed, although the mirror 23 performs an oscillation in a sinusoidal form.

Claims (11)

1. Optical-mechanical scanning system with a movable scanning mirror for the scanning light beam and a downstream lens system for achieving a uniform movement of the scanning point on the scanning plane, characterized in that a sinusoidally oscillating mirror (5, 15, 23) is used and the lens system (6, 16, 22) is given a distortion which compensates for the error with regard to the uniformity of the movement of the scanning point. 2. Scanning system according to claim 1, characterized in that in the case of a non-parallel light beam striking the scanning mirror, the distortion characteristic is given by equation (9) in conjunction with equations (7) and (8). 3. Scanning system according to claim 1, characterized in that for a parallel light beam striking the mirror (5, 15, 23), the distortion characteristic is given by equation (12). 4. Scanning system according to claim 3, characterized in that the lens system (6, 16, 22) has the Seidel distortion coefficient of third order V = 2/3 (1-1/2k[to the power]2) and the distortion coefficient of fifth order where k = 2 is large Phi[low]0 and large Phi[low]0 is the amplitude of the oscillation of the mirror (5, 15, 23). 5. Scanning system according to one of the preceding claims, characterized in that the lens system (6, 16, 22) consists of two subsystems (22a, 22b), one of which is negative and the other positive. 6. Scanning system according to one of claims 1 to 5, characterized in that the lens system (6, 16, 22) has two subsystems which are at a finite distance from one another and each of which has a two-part lens. 7. Scanning system according to one of the preceding claims, characterized in that the lens system (6, 16, 22) has a first subsystem (22a) with negative refractive power arranged towards the mirror (5, 15, 23) and a second subsystem (22b) with positive refractive power arranged towards the scanned surface. 8. Scanning system according to claim 7, characterized in that the refractive indices of the first and second subsystems are n[deep]1 and n[deep]2 respectively and that with a focal length of the lens system of "1", 1.46 less than or equal to n[deep]1 less than or equal to 1.84 and 1.46 less than or equal to n[deep]2 less than or equal to 1.84, the lens system satisfies the following conditions: -5.5 less than or equal to large Psi[deep]1 less than or equal to -0.35 1.2 less than or equal to large Psi[deep]2 less than or equal to 5.7 -10 less than or equal to B[deep]01 less than or equal to 3. where large Psi[deep]1 the refractive power of the first subsystem, large Psi[deep]2 the refractive power of the second subsystem and B[deep]01 is the specific coefficient of the first subsystem, which is given by with r[deep]1 as the radius of curvature of the front lens surface of the first subsystem. 9. Scanning system according to one of claims 1 to 6, characterized in that the lens system has a first subsystem with positive refractive power arranged towards the mirror (5, 15, 23) and a second subsystem with negative refractive power arranged towards the scanned surface. 10. Scanning system according to claim 9, characterized in that the refractive indices of the first and second subsystems are n[deep]1 and n[deep]2 respectively and that with a focal length of the lens system of "1", 1.46 less than or equal to n[deep]1 less than or equal to 1.84 and 1.46 less than or equal to n[deep]2 less than or equal to 1.84, the lens system satisfies the following conditions: 1.35 less than or equal to large Psi[deep]1 less than or equal to 5.5 -5.3 less than or equal to large Psi[deep]2 less than or equal to -0.4 -13 less than or equal to B[deep]01 less than or equal to 4. where large Psi[deep]1 the refractive power of the first subsystem, large Psi[deep]2 the refractive power of the second subsystem and B[deep]01 is the specific coefficient of the first subsystem, which is given by with r[deep]1 as the radius of curvature of the front lens surface of the first subsystem. 11. Scanning system according to one of the preceding claims, characterized in that the lens system (6, 16, 22) has numerical data according to one of the embodiments 1 to 29.