Scanning optical apparatus and image forming apparatus

A scanning optical apparatus comprising:

• a light source;
• a first optical element configured to convert light emitted from the light source into a beam of light;
• a second optical element configured to convert the beam of light having passed through the first optical element into a linear image extending in a main scanning direction;
• a polygon mirror configured to deflect the beam of light having passed through the second optical element in the main scanning direction;
• a third optical element configured to convert the beam of light having been deflected by the polygon mirror into a spot-like image to be focused on a to-be-scanned surface, the third optical element being a single lens having a pair of opposite incident-side and exit-side lens surfaces having first and second optical axes, respectively, each of the pair of opposite lens surfaces being aspheric in a main scanning direction, and having a curvature in a sub-scanning direction varying continuously and symmetrically from a position corresponding to the optical axis thereof outward in a main scanning direction, each of the pair of lens surfaces having a shape symmetric in the main scanning direction with respect to a sub-scanning plane containing the optical axis thereof;
• and
• a synchronization detection beam path configured such that a beam of light having passed therethrough is directed to a sensing element producing a signal for synchronization at a start-of-scan position, the synchronization detection beam path being located on one of two sides out of a range of the deflected beam of light passing through the third optical element, wherein the one of two sides is the same side as that on which the light source is located,
• wherein a distance h between a center of rotation of the polygon mirror and a center of the beam of light incident on the polygon mirror fulfills the following conditions:
• R(sin((α+θeos)/2)−cos((α+θeos)/2)×tan(π/N))+(beos/2)×cos((α+θeos)/2)<h, and
• h<R(sin((α+θbd)/2)+cos((α+θbd)/2)×tan(π/N))−(bbd/2)×cos(α+θbd)/2) (1)
• where R indicates a radius of an inscribed circle of the polygon mirror, N indicates the number of specular surfaces of the polygon mirror, α indicates an angle [rad] formed by the beam of light incident on the polygon mirror with a reference line extending in a direction of travel of the beam of light to be incident on the to-be-scanned surface at right angles after being reflected off the polygon mirror, θbd indicates an angle [rad] formed by the beam of light traveling from the polygon mirror along the synchronization detection beam path with the reference line, θeos indicates an angle [rad] formed by the beam of light reflected off the polygon mirror at an end-of-scan position with the reference line, and beos and bbd indicate breadths of the beam of light in the main scanning direction on each of the specular surfaces of the polygon mirror at the end-of-scan position and at a position in which the beam of light reflected off the polygon mirror travels along the synchronization detection beam path, respectively;
• and
• wherein the third optical element fulfils all of the following conditions:
• −0.59<β1≦0,
• −0.46<β2≦0.2,
• −0.6≦D1<0.43, and
• −0.17≦D2≦0.16
• where β1 indicates an angle [deg] formed in a main scanning plane between the first optical axis and the reference line, β2 indicates an angle [deg] formed in the main scanning plane between the first optical axis and the second optical axis, D1 indicates an amount of shift [mm] in the main scanning plane, of a point of intersection between the first optical axis and the incident-side lens surface, from the reference line, and D2 indicates an amount of shift [mm] in the main scanning plane, of a point of intersection between the second optical axis and the exit-side lens surface, from the first optical axis.