Homogenizer, illuminating optical system, and illuminator

A homogenizer, comprising:

• two convex-lens array pairs each including a first convex-lens array disposed on a light entrance side and a second convex-lens array disposed on a light emission side,
• wherein in each of the convex-lens array pairs, the first convex-lens array and the second convex-lens array are disposed so as to face each other such that each of the convex-lens arrays has a lens surface opposed to each other outward or inward, the first convex-lens array includes a plurality of first convex lenses having a same shape which are disposed in an array arrangement on one surface, each of the first convex lenses is a convex cylindrical lens, the plurality of first convex lenses is disposed such that lens-function axes of the first convex lenses are parallel with each other, the second convex-lens array includes a plurality of second convex lenses having a same shape which are disposed in an array arrangement on one surface, each of the second convex lenses is a convex cylindrical lens, the plurality of second convex lenses is disposed such that lens-function axes of the second convex lenses are parallel with each other, the first convex lenses and the second convex lenses in each of the convex-lens array pairs form convex-lens pairs in each of which the first convex lens and the second convex lens face each other and have a common symmetry axis, the two convex-lens array pairs are serially disposed along an optical-axis direction, which is a traveling direction of incident light, such that the two convex-lens array pairs differ from each other in lens-function axis direction by 90°, in each of the convex-lens array pairs, when a cross-section of each convex lens which is perpendicular to a base-line direction of the convex lens is referred to as a lens cross-section and a position of a symmetry plane in the lens cross-section is referred to as symmetry axis, the first convex lens has an average internal transmission angle for incident light entering a lens-surface center region in the lens cross-section and being in parallel with the symmetry axis, and the average internal transmission angle is equal to or more than 1.3 times an average internal transmission angle in a lens-surface center region of a spherical convex lens having an approximately same maximum diffusion angle as the first convex lens.