Multi-beam scan optical system

A multi-beam scan optical system comprising:

• a laser array including a plurality of laser diodes, said laser diodes having oscillation positions separated from each other by a distance r.sub.1 ;
• a rotating polygen mirror having facets;
• a first scan optical system having an optical axis and including a collimate lens for collimating a plurality of laser beams emitted from the plurality of laser diodes, said collimated laser beams crossing the optical axis of the first scan optical system at a position, each of the laser beams emitted by the laser diodes having a divergence angle .theta..sub.1 which corresponds to an angle within which an intensity of each of the plurality of laser beams is at least 1/e.sup.2 times a maximum intensity of each of the plurality of laser beams in a subsidiary scan direction and a wave length .lambda., a first subsidiary-scan directional power optical member, having an optical power in the subsidiary scan direction, for focusing the collimated laser beams on said facets of said rotating polygon mirror, and an aperture having a diameter and located at the position where the plurality of collimated laser beams cross the optical axis of said first scan optical system;
• and
• a second scan optical system including an f-.theta. lens disposed between the rotating polygon mirror and a photoreceptor surface, said f-.theta. lens receiving laser beams reflected from the rotating polygon mirror and emanating the received laser beams, and a second subsidiary-scan directional power optical member, having an optical power in the subsidiary scan direction, for focusing the laser beams emanated from said f-.theta. lens on the photoreceptor surface in a state that the laser beams are separated from each other by a given interlaced scanning period i in the subsidiary scan direction,
• wherein said parameters r.sub.1, .lambda., .theta..sub.1, and i are selected so as to satisfy the following relation:
• ##EQU5## where K is a number in a range from 1.0 to 1.8, and .alpha. is a value which depends on said diameter of the aperture as viewed in the subsidiary scan direction and satisfies the following relation:
• d.sub.2 =(4.alpha./.pi.)(.lambda.f.sub.2 /D)
• where .pi. is a circular constant, f.sub.2 indicates a focal distance of the first subsidiary-scan directional power optical member, D indicates a diameter in which the intensity is at least 1/e.sup.2 times the maximum intensity of each of the collimated laser beams entering the aperture, where 1/e.sup.2 is a constant, and d.sub.2 indicates a spot diameter in the subsidiary scan direction of each of the laser beams which are focused on the facets of the rotating polygon mirror.