Slit exposure type copying machine capable of copying with anamorphic magnification

A slit exposure type copying machine capable of copying with anamorphic magnification. The degree of the refractive action of at least one triangular prism is so set as to compensate for the difference between the magnification of projection means and the magnification corresponding to the speed of scanning means.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a slit exposure type copying machine, and 
more particularly to such a copying machine for copying with anamorphic 
magnification wherein the image of an original scanned in the form of a 
slit by a scanning system is projected on a photosensitive member through 
a projection lens and at least one triangular prism to form an image on 
the member. 
2. Description of the Prior Art 
Copying machines for giving varying copying magnifications are known 
wherein the projection lens is shifted to the position of magnification of 
.beta.X, with the scanning speed of the scanning system altered to 
V/.beta. (V: peripheral speed of the photosensitive member), to thereby 
obtain a copy at an altered magnification of .beta.X in each of vertical 
and horizontal directions. 
However, copying machines of the type stated for copying anamorphic 
magnification have been proposed in recent years because they are useful 
for designing purposes in varying the vertical-to-horizontal ratio of 
characters and graphic figures, for forming a binding margin along only 
one vertical or horizontal side of copies or for eliminating defects in 
copy images when the forced separation method is used. 
The term "anamorphic magnification" as herein used refers to a method of 
copying the image of an original at a different magnification in each of 
vertical and horizontal directions. 
U.S. Pat. No. 3,445,161, for example, discloses a technique for giving a 
varied vertical-to-horizontal ratio by winding artist's copy and a film 
around drums and projecting the image of the copy on the film through a 
lens and a slit while rotating the copy and film drums at different 
speeds. 
With reference to FIG. 33, it is now assumed that an original 2 placed on 
an original support 11 is to be scanned in the direction of arrow Y along 
the widthwise direction of a slit 3. For the following description, the 
widthwise direction of the slit is defined as the direction of arrow R 
parallel to the scanning direction Y, and the longitudinal direction of 
the slit as the direction of arrow J perpendicular to the scanning 
direction Y. 
The technique of U.S. Pat. No. 3,445,161 will be applied to an 
electrophotographic copying machine in the following manner. The image of 
an original is scanned by a scanning system and then projected by a 
projection lens on a photosenstive drum rotating at a given speed. For 
example, the projection lens is brought to the position of magnification 
of .beta.1X, and the scanning system is set to a scanning speed of 
V/.beta.1.beta.2. The image then formed on the photosensitive drum has a 
magnification of .beta.1X in the slit longitudinal direction and a 
magnification of .beta.1.beta.2X in the slit widthwise direction. The 
image is developed and transferred to paper to afford a copy of anamorphic 
magnification. 
With the above method, however, the peripheral speed of the photosensitive 
drum differs from the speed of the image moving on the drum as will be 
described below, so that the image projected on the drum becomes obscure, 
hence the drawback of reduced resolving power. In other words, it is 
impossible to obtain .beta.2X which differs greatly from 1X, such that the 
.beta.2X actually useful is limited approximately to 1.+-.0.1X. 
The reduction of resolving power mentioned will be described with reference 
to FIG. 1 which shows the operation of a slit exposure type copying system 
wherein the original is adapted to travel. For giving anamorphic 
magnification, a projection lens 1 is placed at the position corresponding 
to a magnification of .beta.1X. An original 2 moves at a speed of 
V/.beta.1.beta.2 across a slit 3 having a width l. A photosensitive member 
4 moves at a speed of V. 
Now, the time t taken for a point A on the original 2 to move over the slit 
3 is 
##EQU1## 
The distance L the photosensitive member 4 moves during the time t is 
EQU L=Vt=.beta.1.beta.2l 
During the time t, on the other hand, the point A of the original 2 moves 
to a point A', and the image formed by the projection lens 1 at the 
position of magnifiction .beta.1X moves from point B to point B' shown. 
The amount of movement, L', of the image is 
EQU L'=.beta.1l 
Thus, while the point A of the original 2 moves to point A', the image 
moves from point B to point B', whereas a point C on the photosensitive 
member 4 moves to point C' (CC'=L). The difference between the image and 
the photosensitive member in the amount of movement results in a reduction 
in resolving power. 
Accordingly, if the image is magnified at .beta.2X only in the slit 
widthwise direction, the amount of movement of the image is 
EQU .beta.2L'=.beta.1.beta.2l=L 
Thus, no difference occurs between the two. 
Published Examined Japanese Patent Application SHO No. 53-28087 discloses a 
cylindrical lens disposed in an optical path as means for eliminating the 
reduction of resolving power and having a refractive power only in the 
scanning direction. Nevertheless, the elongated cylindrical lens has the 
drawback of being difficult and costly to fabricate. 
SUMMARY OF THE INVENTION 
The present invention has been accomplished to overcome all the drawbacks 
of the conventional techniques described above. 
An object of the present invention is to provide a slit exposure type 
copying machine capable of copying with anamorphic magnification which 
comprises moving means for moving a photosensitive member past an exposure 
station at a predetermined speed, means for scanning the image of an 
original in the form of a slit, projection means for projecting the 
scanned original image on the photosensitive member at the exposure 
station to form an image on the member, means for driving the scanning 
means at a scanning speed corresponding to a magnification different from 
the magnification of the projection means, and at least one triangular 
prism disposed in the optical path from the original to the photosensitive 
member for performing a refractive action only in the scanning direction, 
wherein the degree of the refractive action is so set as to compensate for 
the difference between the magnification of the projection means and the 
magnification corresponding to the speed of the scanning means. 
Another object of the present invention is to provide a slit exposure type 
copying machine capable of copying with anamorphic magnification which 
comprises moving means for moving a photosensitive member past an exposure 
station at a predetermined speed, means for scanning the image of an 
original in the form of a slit at a specified speed, a projection lens for 
projecting the scanned original image on the photosensitive member at the 
exposure station to form an image on the member, and at least one 
triangular prism disposed in an optical path in the vicinity of the 
projection lens for performing a refractive action only in one direction. 
As an advantage of the present invention, the copying machine produces very 
sharp copy images although the prism gives different copying 
magnifications in two directions. The present invention has another 
advantage not only in that the prism is less expensive than other 
anamorphic means but also in that a desired anamorphic state can be easily 
selected by varying the number of prisms or by varying the angular 
position of the prism relative to the projection optical path. 
Especially when the prism is in the form of a plate comprising fine prisms, 
the copying machine has the outstanding advantage that the chromatic 
aberration and astigmatism involved can be minimized to produce copy 
images having greatly increased sharpness. 
Other objects and advantages of the present invention will become apparent 
from the following description of embodiments with reference to the 
accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 2 schematically shows an embodiment of copying machine of the 
invention for copying with anamorphic magnification. The machine shown in 
FIG. 2 has a movable original support 11. The support 11 moves at the 
speed to be described later with an original placed thereon. The 
travelling original is illuminated by an illuminating device 12, and the 
image of the original is transmitted to a photosensitive member 4 at an 
exposure station E through a first mirror 13, projection lens 14, second 
mirror 15 and prism 10. The projection lens 14 is movable to the position 
of a desired magnification. The second mirror 15 is shiftable and 
deflectable for accommodating a variation in the length of the optical 
path resulting from the magnification varying movement of the projection 
lens 14. The mechanisms for moving the projection lens 14 and the second 
mirror 15 are known and therefore will not be described. 
With the present embodiment, the speed of the image to be projected on the 
photosensitive member 4 is made to match the speed of movement of the 
member 4 by the action of the prism 10. 
The prism 10, which is a single triangular prism, has approximately the 
same length as the member 4 in its axial direction and is disposed close 
to the member 4. The prism 10 has no refractive action in the slit 
lengthwise direction but performs a refractive action on the slit 
widthwise direction only. The beam emanating from the prism forms an image 
having a height modified by the refractive action relative to the height 
of the image before the incidence. Accordingly the prism can be referred 
to as an optical element which has a magnification only in the direction 
of the refractive action. According to the present invention, the 
magnification of the prism in such only one direction will be termed 
"anamo-magnification" for the sake of convenience. It is to be noted that 
the term "anamorphic magnification" as herein used includes two 
magnifications which are different in vertical and horizontal directions. 
With the arrangement described above, the position of the projection lens 
14 and the scanning speed of the original support 11 are set as listed in 
Table 1 below in which V is the peripheral speed of the photosensitive 
member. 
TABLE 1 
______________________________________ 
Case I Case II 
______________________________________ 
Magnification of projection lens 
.beta.1 .beta.1/.beta.2 
Scanning speed V/.beta.1.beta.2 
V/.beta.1 
Lengthwise magnification 
.beta.1 .beta. 1/.beta.2 
Widthwise magnification 
.beta.1.beta.2 
.beta.1 
______________________________________ 
When the magnification of projection lens and the scanning speed are set as 
listed in Table 1, Case I provides an anamorphic magnification of .beta.1X 
in the slit lengthwise direction and .beta.1.beta.2X in the slit widthwise 
direction, while Case II gives an anamorphic magnification of 
.beta.1/.beta.2X in the slit lengthwise direction and .beta.1X in the slit 
widthwise direction, without entailing a reduction in the resolving power. 
Although the anamo-magnification .beta.2 of the prism is fixed according 
to the present embodiment, the lengthwise magnification or the widthwise 
magnification can be set to a desired value when the speed control 
mechanism for the original support and the mechanism for moving the 
projection lens, etc. are so adapted as to optionally vary the 
magnification .beta.1. 
The anamo-magnification .beta.2 of the prism provided by its refractive 
action as described above will be further described with reference to 
FIGS. 3 to 5. 
FIG. 3 shows two parallel main rays L1 and L2 spaced by a distance h and 
incident on a triangular prism 10 at an angle .theta.1. Principal rays L1 
and L2 advance as refracted as shown. The principal rays are those of 
image forming beams for two image points. Principal rays only will be used 
herein for describing the magnification of image. In this case, there is 
the following relationship according to Snell's law. 
EQU sin .theta.1=n sin .theta.1' (1) 
EQU .theta.2=.alpha.-.theta.1' (2) 
EQU n sin .theta.2=sin .theta.2' (3) 
##EQU2## 
wherein n: refractive index of the prism 
.alpha.: vertex angle of the prism 
.theta.1: angle of incidence on the first surface 
.theta.1': angle of refraction at the first surface 
.theta.2: angle of incidence on the second surface 
.theta.2': angle of refraction at the second surface 
h': spacing between the emerging principal rays 
FIG. 4 shows an image forming position I when the prism is absent. When the 
light forming the image I perpendicular to the principal rays is incident 
on the prism 10 based on the above relationship in this case, the 
principal rays L1, L2 pass through the optical paths of 
P1.fwdarw.Q1.fwdarw.R1.fwdarw.S1 and P2.fwdarw.Q2.fwdarw.R2.fwdarw.S2, 
respectively, to form an image I'. 
The rays passing through a substance having a refractive index n have a 
farther image forming point than those passing through air. Based on the 
relation of equivalent optical path length involved, Q1R1 is selected as 
given below. 
EQU Q1R1=P2Q2/n (5) 
Accordingly P1Q1=x=Q2R2, the equivalent optical path length P1Q1R1 on 
principal ray L1 matches like length P2Q2R2 on principal ray L2. Thus, 
after passing through the prism, R1R2 plane is in equidistance (equivalent 
optical path length) relation with P1P2 plane. 
Now, the deflection of the direction of advance of the principal ray on the 
principal rays L1 and L2 is assumed to be .DELTA.. The magnification 
.beta.2 given by the prism 10 is then 
##EQU3## 
Next with reference to FIG. 5, the line of principal ray L2 after passing 
through the prism is extended into the prism. Suppose the extension has a 
point of intersection U2 with the first surface of the prism, and a 
perpendicular drawn from point R1 to the extension has a foot V2. Since 
.DELTA.S1S2T2 of FIG. 4 is similar to .DELTA.R1R2V2 in FIG. 5, 
EQU .DELTA.=x=Q2V2 (7) 
Further from .DELTA.P1P2Q1, 
EQU x=h tan .theta.1 (8) 
When it is assumed that the foot of a perpendicular drawn from point Q2 to 
principal ray L1 after passing through the prism is W1, 
EQU Q2V2=R1W1=Q1W1-Q1R1 (9) 
From .DELTA.Q1Q2W1, Q1W1 is given by 
EQU Q1W1=h'tan .theta.2' 
Further from Equation (4), 
##EQU4## 
Because Q1R1 has the relationship of Equation (5), P2Q2 can be determined 
as follows from .DELTA.Q1Q2A2 and .DELTA.P2Q2A2, assuming that Q1Q2=k and 
that the foot of a perpendicular drawn from point Q2 to the first plane of 
the prism is A2. 
##EQU5## 
From k which can be expressed as h'/cos .theta.2' and also from Equation 
(4), 
##EQU6## 
From Equations (4), (7), (8), (9), (10) and (11), .beta.2 of Equation (6) 
is given by 
##EQU7## 
In Equation (12), .theta.1', .theta.2 and .theta.2' can be converted to a 
function of .theta.1 from the relationship of Equations (1) to (3). 
Accordingly the anamo-magnification .beta.2 can be determined as desired 
by suitably setting the angle of incidence .theta.1 on the prism, the 
vertex angle .alpha. of the prism and the refractive index n of the prism. 
In the foregoing description, the two principal rays are assumed to be 
parallel for a simplied description. In a general case wherein the rays 
are not parallel, the prism similarly produces a varied magnification, 
which can be determined of course based on the above concept. 
Further the image before incidence on the prism has been handled as being 
perpendicular to the principal rays, but the magnification can be 
similarly determined also when the image is not perpendicular to the 
principal rays. If the image is inclined at an angle of .phi. as indicated 
in a broken line O1P2 in FIG. 4, Equation (12) is modified as follows. 
##EQU8## 
Next, examples of prisms usable for the embodiment of FIG. 2 will be 
described. FIG. 6 shows a prism 10' for obtaining .beta.2 which is 0.89 X. 
In this case, .theta.1=-10.degree.,.alpha.=20.degree. and n=1.5168. 
FIG. 7 shows a prism 10" for giving .beta.2 which is 0.9X. In this case, 
.theta.=0.degree., .alpha.=30.degree. and n=1.5168. 
Further in FIGS. 6 and 7, the prism 10' or 10" may be rotated about an axis 
parallel to the slit lengthwise direction and brought into a reverse 
incidence-emergence relationship to the original. In the case of FIG. 6, 
.beta.2 is then 1/0.89, i.e. 1.12X. At this time, the angle of incidence 
is .theta.1=30.degree.. Similarly in the case of FIG. 7, 
.beta.2=1/0.9=1.11X, and angle of incidence is .theta.1=49.degree.. In 
these cases, the image before the incidence on the prism is not 
perpendicular to the principal rays. 
With the anamorphic copying machine of the present invention, the prism 10 
may be disposed at any location in the optical path. Whereas the prism 10 
is disposed on one side of the projection lens 14 in FIG. 2, the prism is 
disposed on the other side of the lens toward the original according to 
the embodiment of FIG. 8. 
FIG. 9 shows an embodiment incorporating a bundle 20 of optical fibers 
having graded refractive indexes as a projection optical system. This 
embodiment, in which the bundle 20 has a fixed magnification, affords 
anamorphic magnigication according to Case I. 
When copying machines including the above anamorphic magnification 
mechanism are to be used in the usual mangification varying mode, the 
prism is retracted from the optical path, and the variation in the length 
of the optical path and the inclination of the path are corrected. 
Alternatively, the prism is rotated to set the magnification provided by 
the prism to 1X. 
Next, an embodiment will be described which includes at least one prism 10 
as in FIG. 2 and means for varying the angle of incidence of a beam on the 
prism 10. The anamomagnification .beta.2 of the prism is varied by varying 
the angle of incidence on the prism by one of the following two means 
which are relatively the same. The first is means for rotating the prism 
itself about an axis parallel to the slit as schematically shown in FIG. 
10. With reference to FIG. 10, the prism 10 is rotated from position A to 
position B through an angle .theta.L. The angle of incidence .theta.1a at 
the position A and the angle of incidence .theta.1b at the position B then 
have the following relationship therebetween. The angle in a 
counterclockwise direction is assumed to be positive. 
EQU .theta.1b=.theta.1a-.theta.L (13) 
This equation and Equations (1) to (3) give .theta.1b', .theta.2b and 
.theta.2b' when the initial angle of incidence .theta.1a and the angle of 
rotation .theta.L are given. Substitution of these values in Equation (12) 
or (12)' affords the magnification .beta.2b at the position B. Preferably 
the center of rotation is so selected as to minimize the displacement of 
the image forming position, inclination of image and variation in the 
length of the optical path due to the rotation. 
The second means is adapted to vary the angle of incidence by shifting the 
optical path for the beam incident on the prism, with the prism 10 in 
fixed position, as schematically shown in FIG. 11. For a simplified 
description, FIG. 11 shows that the shifted optical path or principal rays 
L1', L2' are incident on the prism perpendicular thereto. 
The optical path is thus shifted by pivotally and otherwise moving a front 
reflecting system, e.g. the second mirror 15 in FIG. 2. Preferably such 
movement is also so effected as to minimize the displacement of the image 
forming position, inclination of image and variation in the length of the 
optical path. 
Of course, it is possible to use the foregoing first and second means in 
combination. 
Since these first and second means are relatively the same, variations in 
the magnification .beta.2 resulting from variations in the angle of 
incidence .theta.1 are given in Table 1, in which a prism I has a vertex 
angle of 30.degree. and a prism II has a vertex angle of 15.degree.. The 
two prisms have a refractive index n of 1.5168. 
TABLE 2 
______________________________________ 
Angle of incidence 
Magnification .beta.2 
Magnification .beta.2 
.theta.1 Prism I Prism II 
______________________________________ 
-15 0.66 0.86 
-10 0.76 0.90 
-5 0.84 0.93 
0 0.90 0.95 
5 0.95 0.97 
10 1.00 0.99 
15 1.04 1.00 
20 1.08 1.03 
25 1.13 1.05 
30 1.18 1.08 
______________________________________ 
The embodiments described comprise a single prism, whereas use of two 
prisms is advantageous in various aspects. Stated more specifically, a 
single prism permits occurrence of chromatic aberration and astigmatism 
and forms a greatly inclined image, but astigmatism can be diminished with 
use of two prisms having a smaller vertex angle than the single prism. 
Further two prisms can be arranged with their vertex angles oriented in 
opposite directions for each to offset the chromatic aberration and 
inclination of image of the other. FIG. 12 shows a case wherein two prisms 
10A and 10B are used. Indicated at h1 is the distance between the 
principal rays before incidence on the prism 10A, at h2 the distance 
between the principal rays within the prism 10A, at h3 the corresponding 
ray-to-ray distance between the two prisms 10A and 10B, at h4 the distance 
between the principal rays within the prism 10B, and at h5 the distance 
between the principal rays emerging from the prism 10B. These ray-to-ray 
distances have the following relationships therebetween. The angle of 
incidence, angle of refraction and vertex angle of each prism satisfy the 
relationship of Equations (1) to (3). 
##EQU9## 
When h5 is determined from Equations (14) and assuming that the 
displacement of the principal rays emerging from the prism 10B is 
.DELTA.', the eventual magnification .beta.20 is given by 
##EQU10## 
The displacement of principal rays, .DELTA.', can be determined in the 
same manner as in the foregoing case of single prism. The broken lines 
E1E2, F1F2 and G1G2 shown represent inclinations of the image. It is seen 
that the eventual inclination of the image is much smaller than is the 
case with a single prism. 
More specifically the inclination of image is obtained in the following 
manner. With reference to FIG. 3, it is assumed that the deflection angle 
of angle of emergence relative to the angle of incidence is .epsilon.. 
Then this angle is given by 
EQU .epsilon.=.theta.1.multidot..theta.2'-.alpha. 
On the other hand, when the inclination angle of the image surface relative 
to the principal rays is .omega., 
##EQU11## 
Accordingly the inclination angle .eta. of the image surface after passing 
through the prism relative to the image surface before passing through the 
prism is 
##EQU12## 
By repeating this a number of times equal to the number of prisms, the 
eventual inclination angle of the image surface can be obtained. 
The system of a plurality of prisms is advantageous over a single prism in 
that the former is smaller in the inclination of image surface as 
described above and is further lesser in astigmatism and chromatic 
aberration. 
Next, astigmatism will be described. Astigmatism is the phenomenon that 
light emanating from a point light fails to form an image at one point 
when passing through an image forming optical system. This occurs because 
the meridional beam and the sagittal beam converge at different points. 
The difference between the points of convergence of the two beams is 
termed astigmatic difference. 
With reference to FIG. 23, suppose light from a light source O advances as 
refracted at points P and Q. Further suppose the virtual points of 
convergence of the meridional beam and sagittal beam refracted at Q are Om 
and Os, respectively, OP=P1 and PQ=d. The distances from Q to the points 
of convergence of the meridional beam and sagittal beam are 
##EQU13## 
Accordingly the astigmatic difference .DELTA.P is 
##EQU14## 
For details of this calculation, refer to Hiroshi Kubota, "Kohgaku 
(Optics)," Iwanami-shoten, Japan. 
Now with reference to Equation (18), a single prism and a two-prism system 
will be compared when giving the same magnification. With the two-prism 
system, the angle of incidence and the angle of refraction at the planes 
concerned can be smaller than is the case with the single prism. 
Accordingly the cosine terms of Equation (18) are approximate to 1, with 
the result that .DELTA.P is small. 
Further it is noted that chromatic aberration is a dispersion phenomenon 
resulting from the fact that the refractive index differs for different 
wavelengths. When two prisms are so arranged that their vertex angles are 
oriented in opposite directions as seen in FIG. 12, the rays of different 
wavelengths are dispersed by the first prism and then dispersed by the 
second prism in opposite direction, so that the rays are consequently 
converged. Thus, chromatic aberration can be made smaller by the two-prism 
system. 
As described above, the system of a plurality of prisms has the advantage 
over single prisms that it is lesser in the inclination of image surface, 
astigmatism and chromatic aberration. 
Next, a preferred embodiment of system of plural prisms will be described. 
FIG. 24 shows an arrangement of two prisms 10A and 10B having a vertex 
angle of 15.degree. for giving a magnification of 0.9X. The angle of 
incidence on the first surface of each prism is 0.degree.. Now, Pm and Ps 
of Equations (16) and (17) for the prisms 10A and 10B will be represented 
by these symbols with the adscripts of a and b. Suppose the thicknesses of 
the prisms through which the beam passes are da, db, the prism-to-prism 
distance the beam passes is dab, and the refractive index is 1.5. From 
Equations (16), (17) and (18), 
##EQU15## 
For the beam passing through the prism 10B after passing through the prism 
10A, 
##EQU16## 
Accordingly the astigmatic difference .DELTA.P is 
EQU .DELTA.P=Pmb-Psb=0.2Pl-(0.13da+0.06db+0.1dab) 
Now, suppose Pl=10 mm, da=2.57 mm and a beam passes through the prisms 
toward one end of the prism 10A opposite to its vertex angle for the sake 
of simplicity. dab and db are then smaller than da, so that .DELTA.P at 
this time is 
EQU .DELTA.P.perspectiveto.1.7 
For comparison, a case is considered in which a a single prism having a 
vertex angle of 30.degree. and a refractive index of 1.5 is used, and a 
beam is made incident on the first surface thereof perpendicular thereto 
to give a magnification of 0.9. When Pl=10 mm as in the above case, 
.DELTA.P' obtained is 
EQU .DELTA.P'.perspectiveto.7.1 
Apparently the two-prism system is smaller in astigmatic difference than 
the single prism. 
FIGS. 13 to 15 show embodiments having the same construction as the one 
shown in FIG. 2 except that such two prisms are arranged within the 
copying machine. 
When these two prisms are used, the anamo-magnification can be varied in 
the following manner. 
______________________________________ 
Prism 10A Prism 10B 
______________________________________ 
(i) Fixing Rotating 
(ii) Rotating Fixing 
(iii) 
Rotating Rotating 
(iv) Fixing Varying angle of incidence 
(v) Varying angle of incidence 
Fixing 
(vi) Varying angle of incidence 
Varying angle of incidence 
______________________________________ 
"Varying angle of incidence" in (iv), (v) and (vi) means that the path for 
the beam to be incident on the prism concerned is shifted with the prism 
fixed. Since this is substantially difficult with the systems of FIGS. 13 
and 14 wherein the two prisms are closely arranged, this method may be 
used for the arrangement of FIG. 15 wherein the two prisms are away from 
each other. In FIG. 15, the prism 10A is interposed between the original 
support 11 and the first mirror 13, and the prism 10B between the second 
mirror 15 and the photosensitive member 4. 
(i) and (ii), (iii) and (iv), and (v) and (vi) can be regarded as 
relatively the same condition. 
Listed below are magnifications .beta.2 and angles of inclination of image, 
.theta.G, when the vertex angles of the prisms 10A, 10B and the angle of 
incidence on the prism 10A are predetermined, and the angle of incidence 
.theta.3 on the prism 10B is varied by rotating the prism 10B. The angle 
of inclination of an image, .theta.G, is the angle formed between the 
image before incidence on a prism and the image emerging from the prism. 
With reference to FIG. 12, the angle between E1E2 and G1G2 is this angle. 
TABLE 3 
______________________________________ 
.theta.3 
.beta.2 
.theta.G 
______________________________________ 
-15 0.30 -2.66 Vertex angle of prism 10A: 30.degree. 
-10 0.50 -4.76 Vertex angle of prism 10B: 30.degree. 
-5 0.62 -4.45 Angle of incidence on prism 10A: 15.degree. 
0 0.70 -3.96 Angle of emergence from prism 10A: 31.54.degree. 
5 0.76 -3.44 
10 0.81 -2.90 
15 0.86 -2.33 
20 0.90 -1.71 
25 0.94 -1.02 
30 0.99 -0.25 
______________________________________ 
TABLE 4 
______________________________________ 
.theta.3 
.beta.2 
.theta.G 
______________________________________ 
-15 0.86 -0.13 Vertex angle of prism 10A: 15.degree. 
-10 0.90 -0.22 Vertex angle of prism 10B: 15.degree. 
-5 0.92 -0.25 Angle of incidence on prism 10A: 10.degree. 
0 0.95 -0.23 Angle of emergence from prism 10A: 12.85.degree. 
5 0.97 -0.18 
10 0.98 -0.08 
15 1.00 0.07 
20 1.03 0.25 
25 1.05 0.48 
30 1.08 0.76 
______________________________________ 
TABLE 5 
______________________________________ 
.theta.3 
.beta.2 
.theta.G 
______________________________________ 
-15 0.88 -0.01 Vertex angle of prism 10A: 15.degree. 
-10 0.91 -0.08 Vertex angle of prism 10B: 15.degree. 
-5 0.94 -1.20 Angle of incidence on prism 10A: 15.degree. 
0 0.97 -1.07 Angle of emergence from prism 10A: 7.86.degree. 
5 0.99 -0.05 
10 1.01 0.05 
15 1.03 0.19 
20 1.05 0.37 
25 1.07 0.60 
30 1.10 0.87 
______________________________________ 
TABLE 6 
______________________________________ 
.theta.3 
.beta.2 
.theta.G 
______________________________________ 
-15 0.82 0.45 Vertex angle of prism 10A: 14.degree. 
-10 0.85 0.30 Vertex angle of prism 10B: 16.degree. 
-5 0.88 0.22 Angle of incidence on prism 10A: 0.degree. 
0 0.91 0.20 Angle of emergence from prism 10A: 21.53.degree. 
5 0.93 0.23 
10 0.95 0.32 
15 0.97 0.45 
20 0.99 0.62 
25 1.02 0.84 
30 1.04 1.11 
______________________________________ 
The data listed above reveals the tendency that the magnification increases 
with an increase in the vertex angle of the prism and also with an 
increase in the angle of incidence. When two prisms are used, a greater 
magnification is obtained when the vertex angle of the rear prism is 
larger than that of the front prism. 
Thus according to the present embodiment, the anamorphic magnification 
provided by one or at least two prisms is varied by altering the relative 
angle of incidence of light on the prism. In practice, it is advantageous 
in respect of precision and cost to consider a combination of several 
expedients, such as positioning the eventual image in parallel with the 
object plane, use of a plurality of prisms having the same vertex angle 
and setting the angle of incidence to 0.degree.. 
With reference again to Equations (12) and (12)', it is seen that the 
anamo-magnification is variable also by altering the vertex angle, i.e. by 
selectively positioning one of a plurality of prisms having different 
vertex angles in the optical path. Furthermore, the magnification is 
variable by selectively using one of a plurality of prism systems which 
are different in vertex angle and the relative angle of incidence on which 
is variable. 
FIG. 16 schematically shows an embodiment of anamorphic copying machine 
wherein a prism 10 is disposed in the vicinity of a projection lens 14. 
Like the copying machine shown in FIG. 2, this machine comprises an 
illuminating device 12 for illuminating originals, first mirror 13, 
projection lens 14, prism 10, second mirror 15 and a photosensitive member 
4 at an exposure station E. This machine differs from the one shown in 
FIG. 2 in that the prism 10 is disposed in the vicinity of the projection 
lens in the optical path of projection. The prism 10 has nearly the same 
size as the projection lens 14, has no refractive action in the slit 
lengthwise direction but performs a refractive action only in the slit 
widthwise direction to give an anamo-magnification of .beta.2. When so 
positioned as stated above, the prism can be of a greatly reduced size 
which is approximately the size of the projection lens. 
With the arrangement described, the magnification .beta.2 of the prism can 
be determined in exactly the same manner as described for the embodiment 
of FIG. 2. Thus the magnification can be calculated from Equation (12) 
when the image before the incidence on the prism is perpendicular to the 
principal rays, or from Equation (12)' when the image before incidence is 
not perpendicular to the principal rays but is inclined at an angle .psi.. 
From a different viewpoint, the present embodiment, in which the prism is 
disposed in the vicinity of the projection lens, gives anamorphic 
magnification with greater ease, i.e. by rotating the prism through 
90.degree. about the optical axis of the projection lens. FIG. 17A shows 
an arrangement corresponding to FIG. 16. A slit illumination zone S is 
shown, with the first, second mirrors, etc. omitted. FIG. 17B shows the 
same arrangement, in which the prism 10 has been rotated through 
90.degree. from the position in FIG. 17A. In the state of FIG. 17B, the 
prism performs a refractive action in the slit lengthwise direction but no 
refractive action in the slit widthwise direction. In this case, in the 
slit widthwise direction, the absence of refractive action produces no 
vairation in magnification and therefore no reduction in resolving power, 
so that the scanning speed is in the usual relationship with the 
projection lens. Stated more specifically, if the projection lens in the 
position of magnification .beta.1, the scanning speed is V/.beta.1, making 
it possible to obtain copies which have a magnification of .beta.1.beta.2X 
in the slit lengthwise direction and a magnification of .beta.1X in the 
slit widthwise direction. Since the position of the projection lens is 
related to the scanning speed for the usual mode of magnification 
variation, the arrangement can be adapted for anamorphic magnification 
with ease. 
Further in the case of FIG. 17B, the image is deviated toward one side 
axially of the photosensitive member. This is illustrated in FIG. 18 which 
is a development of the optical path. Accordingly the arrangement is 
advantageous for simple uses for forming a binding margin or forming a 
blank area for forced separation. 
The arrangement wherein the prism is rotatable about the optical axis of 
the projection lens so as to be selectively positioned in the state of 
FIG. 17A or 17B has another advantage. In the case of reduced anamorphic 
magnification, Case I or Case II (FIG. 19 (a)) in Table 1 is selectable 
when it is desired to obtain copies which are on a reduced scale in the 
slit widthwise direction. Further when it is desired to obtain copies 
which are on a reduced scale in the slit lengthwise direction, with the 
copy image deviated toward one side in the slit lengthwise direction (FIG. 
19 (b)), the state of FIG. 17B is to be selected. Thus the arrangement is 
suited for such selective use. When the prism is made reversibly 
rotatable, the image can be deviated selectively toward either side of 
paper. 
In the present embodiment wherein the prism is disposed close to the 
projection lens, the prism itself can be made rotatable about an axis 
parallel to the slit lengthwise direction to provide an altered 
anamo-magnification. Preferably the axis of rotation is so selected as to 
minimize the deviation of image forming position, inclination of image and 
variation in the length of the optical path due to the rotation. 
The above magnification is variable similarly also in the case of FIG. 17B. 
In this case, moreover, the position of the image is shiftable in the slit 
lengthwise direction insofar as a definite relationship is maintained 
between the magnification and the position. 
The two-prism system described with reference to FIG. 12 is more 
advantageous than the single-prism system described with reference to FIG. 
10, as already stated. 
Accordingly when the prism 10 of FIG. 16 is replaced by the two-prism 
system described, aberrations, etc. can be corrected to afford copy images 
of improved quality. 
Furthermore, the two-prism system 10' is made rotatable exactly in the same 
manner as the prism shown in FIG. 17, i.e. from the state of FIG. 20A to 
the state of FIG. 20B. 
In the case of the two-prism system 10', moreover, only one of the prisms 
can be rotated to the state of FIG. 20C or to the state of FIG. 20D. As in 
Table 1, Table 7 shows the magnification of the projection lens, scanning 
speed and lengthwise and widthwise magnifications in this case. 
TABLE 7 
______________________________________ 
Case I Case II 
______________________________________ 
Magnification of projection lens 
.beta.1 .beta.1/.beta.2A 
Scanning speed V/.beta.1.beta.2A 
V/.beta.1 
Lengthwise magnification 
.beta.1.beta.2B 
.beta.1.beta.2B/.beta.2A 
Widthwise magnification 
.beta.1.beta.2A 
.beta.1 
______________________________________ 
In the present arrangement, the fixed prism 10A toward the projection lens 
has a magnification of .beta.2A, and the rotatable prism 10B a 
magnification of .beta.2B. 
In this way, rotation of one of the prisms only gives anamorphic 
magnification involving different vertical-to-horizontal ratios, with the 
copy image deviated toward one side, and an increased number of different 
vertical-to-horizontal ratios are available. 
Further with the two-prism system 10', as in the case of a single prism, 
one or both of the prisms can be rotated about an axis parallel to the 
ridgeline to vary the magnification (see FIG. 20A). The magnification can 
be calculated by applying the method used for the foregoing case of single 
prism. Additionally, the two-prism system is usable in the following 
manner. When an arrangement including a single prism is to be returned to 
the usual mode of varying magnification, there is the need to retract the 
prism from the optical path and to correct the resulting variation in the 
length of optical path, etc., whereas with the two-prism system, a 
refractive power for the magnification of 1X can be obtained by suitably 
setting the angle of incidence and vertex angle of the prism without the 
necessity of correcting the length of optical path. FIG. 21B shows prisms 
10A and 10B as moved to give the magnification of 1X. Further when having 
the same vertex angle, the two prisms can be joined together as shown in 
FIG. 21C, with the incidence surface and the emergence surface positioned 
perpendicular to the optical axis of the projection lens, whereby the 
system can be made equivalent to a planar glass plate having no refractive 
power. 
Table 8 shows data relating to the arrangement of FIGS. 21A and 21B, in 
which the vertex angle and refractive index of each prism is 15.degree. 
and 1.5168, respectively. The inclination of image surface, .DELTA.', is 
calculated from Equations (14) and (15). The angles of incidence on the 
prisms 10A and 10B are represented by .theta.1 and .theta.3, respectively. 
TABLE 8 
______________________________________ 
FIG. 21A 
FIG. 21B 
______________________________________ 
Angle of incidence .theta.1 
0.degree. 11.4.degree. 
Angle of incidence .theta.3 
0.degree. -11.4.degree. 
Magnification 0.91 1 
Inclination of image surface .DELTA.' 
-0.01h' 0 
______________________________________ 
FIG. 22 shows that the position of image can be altered by shifting a prism 
10 in the direction in which it has a refractive power. In the case of 
FIG. 18, this adjusts the blank area Z. The deviation of image forming 
position produced when the prism is rotated can be corrected by the shift 
of the prism. 
Finally, FIG. 26 shows an embodiment of anamorphic copying machine 
incorporating a prism plate which is an assembly of fine prisms. The 
copying machine includes a movable optical system. Thus, a scanning system 
9 comprising an illuminating device 12 and first to third mirrors 6, 7, 8 
is moved along the bottom surface of an original support 11, whereby the 
image of an original on the support 11 is scanned in the form of a slit. 
The scanned image is projected through a projection lens 14 and a fourth 
mirror 15' onto a photosensitive member 4 at an exposure station E to form 
an electrostatic latent image on the photosensitive member 4. A copy image 
corresponding to the latent image is obtained by depositing a toner on the 
member 4, transferring the toner image to copy paper and fixing the 
transferred toner image. 
The projection lens 14 is movable axially thereof by a stepping motor or 
the like and can be held in a desired position to copy the image of the 
original at a desired altered magnification in both vertical and 
horizontal directions. 
The speed of of the drive system for the scanning system 9 is variable by a 
d.c. motor or the like. Thus, the scanning speed of the scanning system 9 
is varied to alter the ratio of this speed to the speed of movement of the 
photosensitive member 4, whereby the copying magnification in the slit 
widthwise direction is varied relative to that in the slit lengthwise 
direction. This realizes copying with anamorphic magnification, i.e. with 
different magnifications in the vertical and horizontal directions. 
According to the present embodiment, a prism plate 10" in the form of an 
assembly of fine prisms is provided between the fourth mirror 15' and the 
photosensitive member 4 to obtain a match between the speed of the image 
to be projected on the member 4 and the speed (peripheral speed) of 
movement of the member 4. 
The prism plate 10", which has approximately the same length as the 
photosensitive member 4, is disposed in the vicinity of the member 4. The 
prism plate 10" has no refractive action in the slit lengthwise direction 
but performs a refractive action only in the slit widthwise direction and 
therefore has an anamo-magnification of .beta.2 in this direction. 
With the embodiment described, the position of the projection lens 14 and 
the original scanning speed when the peripheral speed of the 
photosensitive member is V are set to the values listed in Table 1 for two 
cases I and II, as is the case with the embodiment of FIG. 2. 
The arrangement of the present embodiment including the prism plate 10" 
will be described further with reference to FIG. 27. The magnification 
.beta.PL of the prism plate and the angle of rotation of image, .omega.PL, 
can be calculated from Equations (19), (20) and (21) to follow, using the 
angle of incidence of the principal beam on the prism plate 10" and the 
inclination of image relative to the incident principal beam as main 
parameters. 
##EQU17## 
In the above equations: h, hPL: height of image within the principal beam 
.phi., .phi.PL: inclination of image relative to the principal beam 
.epsilon.: angle of refraction given by the prism plate 
.psi.: angle of incidence on the prism plate 
.psi.': angle of emergence from the prism plate .psi.'=.psi.-.epsilon. 
Of the parameters given above, those representing angles are positive when 
clockwise. 
FIG. 28 shows on an enlarged scale a portion of the prism plate 10" in the 
form of an assembly of fine prisms. In this diagram, .alpha., .theta.1, 
.theta.2', .epsilon., .psi., .psi.', .phi. and .phi.PL are in common with 
those shown in FIGS. 3, 4, 5 and 27. Represented by .phi.PR is the 
inclination of image with respect to the principal rays in each fine 
prism, and by .gamma. is the angle between the incidence surface of each 
fine prism and the prism plate (positive when clockwise with respect to 
the prism plate). 
There are the following relations. 
EQU .psi.=.gamma.+.theta.1 (22) 
EQU .psi.'=.theta.1'-.gamma.-.alpha. (23) 
(In FIG. 28, .psi.' is negative.) 
The rotational angle of image, .omega.PR, in each fine prism is 
EQU .omega.PR=.phi.PR-.phi.-.epsilon. (24) 
wherein 
##EQU18## 
The prism plate 10" gives anamorphic magnification when the following 
equation is satisfied. 
EQU .beta.PR cos.phi.PR=.beta.PL cos.phi.PL (26) 
This means that in view of Equations (22) and (23), there is no condition 
which satisfies both (12)'=(19) and (24)=(20) (i.e. (25)=(21)) at the same 
time. 
Thus, from Equations (12)', (19), (21), (22), (23) and (25), .gamma. is to 
be determined which has the relation of 
##EQU19## 
(The angle .gamma. is not dependent on .phi..) Equation (10) gives such 
.gamma.. 
##EQU20## 
Equation (26) indicates that the differences between the prism plate and 
single prisms in magnification and image rotation are allowable if the 
width of the principal beam is large to some extent as compared with the 
size of the single prisms. 
In practice, the angular difference of image rotation only matters, but 
when this is regarded as astigmatism, the value is smaller than in the 
case of anamorphic magnification given by the single prism of FIG. 3. 
With reference to FIG. 28, the eclipse of beams will be described. An 
eclipse occurs because the prism has a surface (surface A in FIG. 28) 
which does not produce the action of prism. 
However, with slit scanning optical systems generally used for plain paper 
copier or the like, an eclipse, even if occurring, creates no defect in 
copy images as far as the scanning direction (direction perpendicular to 
the slit lengthwise direction) is concerned, because in the scanning 
direction, a point on the original moves perpendicular to the slit 
lengthwise direction and is exposed to light and projected on the 
photosensitive member during travel over the width of the slit. 
Accordingly, even if a prism plate which eclipses the beam is positioned 
in the scanning direction, the plate permits exposure, merely resulting in 
a reduced amount of exposure. It is therefore desirable to eliminate the 
eclipse if possible, to remedy the reduction in the amount of exposure due 
to the eclipse. 
An eclipse caused by a surface of the prism plate on the incidence side 
thereof will be described further with reference to FIGS. 29A and 29B. The 
surface corresponds to the surface A in FIG. 28 and is so prepared as to 
be positioned in parallel with the incident beam. FIG. 29A shows a case 
wherein .theta.1&gt;0, and FIG. 29B shows a case wherein .theta.1&lt;0. The 
incident beam is eclipsed in either case. To eliminate the eclipse, there 
is a need to make .theta.1 equal to 0 (i.e. to render the beam incident on 
the prism surface perpendicular thereto) or to render the incidence 
surface planar. 
FIGS. 30A and 30B each show a prism plate 10" one surface of which is 
planar. In FIG. 30A, .gamma.=0, and in FIG. 30B, .gamma.=-.alpha.. In each 
of these cases, Equation (27) leads to the following relationship. 
When .gamma.=0: 
##EQU21## 
Therefore, cos .theta.1' cos .theta.2'=cos .theta.2 cos(.theta.2'-.alpha.) 
However, from 
EQU .theta.1'=.theta.2+.alpha., 
EQU cos(.theta.2+.alpha.).multidot.cos .theta.2'=cos 
.theta.2.multidot.cos(.theta.2'-.alpha.) 
EQU -sin .theta.2.multidot.cos .theta.2' sin .alpha.=cos .theta.2.multidot.sin 
.theta.2' sin .alpha. 
EQU sin .theta.2.multidot.cos .theta.2'+cos .theta.2 sin .theta.2'=0 (since sin 
.alpha..noteq.0) 
Hence, sin (.theta.2+.theta.2')=0 
EQU .theta.2+.theta.2'=0 
On the other hand, from Snell's law, nsin .theta.2=sin .theta.2', and 
n.noteq.1, so that 
EQU .theta.2=.theta.2'=0 
When .gamma.=-.alpha.: 
Similarly, 
EQU cos .theta.1' cos(.theta.1-.alpha.)=cos .theta.1 cos .theta.2 
EQU cos .theta.1' cos(.theta.1-.alpha.)=cos .theta.1 cos(.theta.1'-.alpha.) 
Therefore, sin(.theta.1-.theta.1')=0 
Hence, .theta.1=.theta.1'=0 (since n.noteq.1) 
Thus the eclipse can be inhibited very advantageously by using the prism 
plate 10" for giving anamorphic magnification as shown in FIGS. 30A or 30B 
wherein when the incidence side is planar as seen in FIG. 30A, each 
component prism is adapted to emanate rays perpendicular to its surface on 
the opposite side, or when the emergence side is planar as seen in FIG. 
30B, the incidence surface of each component prism is arranged 
perpendicular to incident rays. When the prism plate 10" in the form of an 
assembly of fine prisms has one plane surface and the other surface which 
is provided by surfaces of the prisms as illustrated, the prism plate has 
the advantage of being easier to fabricate than the one shown in FIG. 28 
which is a simple assembly of fine prisms arranged one above another. 
FIGS. 31 and 32 each show an arrangement of two prism plates each having a 
plane surface and a composite prism surface. These arrangements are useful 
for inhibiting eclipses and are also advantageous for greatly diminishing 
chromatic aberration and astigmatic difference. 
The present invention is not limited only to the illustrated construction 
of prism plates 10". 
Although the present invention has been described above as embodied as 
copying machines of different types having a slit exposure system, it is 
apparent that the embodiments described are usable for copying machines, 
having a slit exposure system, of any type, i.e. original support movable 
type, scanning system movable type or original movable type.