A scanning system utilizes a randomly addressable image sensor which is selectively positioned at the Scheimpflug angle in the image plane in order to detect focused light reflected from an object. Light reflected from the object is focused onto the sensor through an objective lens. Since the sensor is mounted at the Scheimpflug angle, each strip within the depth of field of the object plane has corresponding pixels on the sensor which are in focus.

A pupil conjugate-coupling device in a projecting optical system includes a first projection lens system which forms an intermediate image of an image indicating element, a second projection lens system which projects the intermediate image onto a screen, said first and second projection lens systems having optical axes intersecting at a predetermined angle, and an optical element having structural periodicity positioned between the first and second projection lens systems. The optical element has a positive power and a prism function for deflecting a bundle of rays transmitted through the first projection lens system towards the optical axis of the second projection lens system to thereby couple pupils of the first and second projection lens systems. The optical element is deviated from an intermediate image forming position by a predetermined offset in the optical axis direction thereof.

An optical system projects an enlargement of an image of an object surface on a screen inclined relative to the object surface. The optical system includes an afocal first lens unit including a diaphragm and at least a second lens unit. The optical axis of the afocal system is not collinear with a normal line from the object surface, i.e., the afocal system is eccentric to the object surface. The second lens unit is eccentric relative to the afocal lens unit.

A projection optical device includes a projection optical system for projecting an image of an object plane onto a screen without forming an intermediate real image. The projection optical system includes a coaxial first lens group to be arranged relatively near the object plane, a coaxial second lens group to be arranged relatively near the screen, and a stop arranged between the first and second lens groups. The second lens group has an optical axis inclined with respect to an optical axis of the first lens group. A magnification .beta.1 of the first lens group satisfies a relationship of .vertline.1/.beta.1.vertline.<0.05. The second lens group is angularly deviated from the first lens group around a position of the stop.

To provide an oblique projection type displaying apparatus for radiating rays of light which are nearly parallel with a light bulb, thereby preventing the brightness of a resultant image from becoming uneven, the apparatus comprises a light source, optical modulating means, projecting means for projecting an image generated by the optical modulating means on a screen, and the screen, wherein a center optical axis of rays of light projected by the projecting means are obliquely entered into the screen, wherein the projecting means comprises first projecting optical means for converting an image generated by the optical modulating means into an intermediate image with trapezoidal distortion, and second projecting optical means for converting the intermediate image with trapezoidal distortion into an image without trapezoidal distortion on the screen, and wherein the first projecting optical means comprises two lenses which are not parallel each other. In addition, the constructions of the light source, the reflection mirror for changing the optical path, and the screen are modified.