An interferometer is often used to measure the surface accuracy of optical components, such as optical lenses or mirrors. In particular, a Fizeau interferometer, which is equipped with a reference lens that is normally manufactured with a high degree of accuracy, is widely used as an interferometer because it has a simple structure, a comparatively wide field of view, and can measure a surface shape with high accuracy.
With a Fizeau interferometer, the measurement of a spherical surface (hereinafter referred to as a xe2x80x9csubject spherical surfacexe2x80x9d), such as a lens surface, is performed as follows. First, a parallel incident luminous flux defining a collimated light beam with a planar wavefront is converged by a reference lens into a spherical light wave. Then, the spherical light wave strikes a subject spherical surface. The optical arrangement is designed so that directions normal to the spherical light wave (that define the directions of convergence of the spherical surface light wave) coincide with the directions normal to the subject spherical surface. This results in the light being reflected backwards in directions exactly opposite to its directions of incidence onto the subject spherical surface. This light is hereinafter referred to as the xe2x80x9csubject lightxe2x80x9d, and it then passes once more through the reference lens. However, not all the light that enters the reference lens which is directed toward the subject spherical surface actually reaches the subject spherical surface. A portion of the incident light beam (hereinafter referred to as the xe2x80x9creference lightxe2x80x9d) is reflected from the spherical lens surface of the reference lens that is nearest the subject spherical surface (hereinafter referred to as a xe2x80x9creference spherical surfacexe2x80x9d) and passes back through the reference lens. The subject light and the reference light interfere to create interference fringes. Observation of these interference fringes enables the measurement of the shape of the subject spherical surface.
With this Fizeau interferometer, in order to fully measure the subject spherical surface that has an acceptance angle xcex81 (the angle that the outer edge portions of the subject spherical surface make with the center of curvature of the subject spherical surface), it is necessary that the light beam with the spherical wavefront be converged by a collection angle xcex82 that is larger than the acceptance angle xcex81. In other words, it is necessary to satisfy the relationship: xcex82 greater than xcex81. A more detailed explanation is as follows. The relationship between the collection angle xcex82 and the numerical aperture NA of the reference lens at the light incident side of the subject spherical surface is expressed as follows:
NA=sin (xcex82/2). 
On the other hand, the maximum diameter B of a subject spherical surface about the optical axis, the radius of curvature C of the subject spherical surface, and the acceptance angle xcex81, are related as follows for full measurement of the subject spherical surface:
B/(2C)=sin (xcex81/2 ). 
Additionally, in order to satisfy the relationship xcex82 greater than xcex81, it follows that:
sin (xcex82/2) greater than sin (xcex81/2). 
Consequently, in order to fully measure the subject spherical surface, a relatively large numerical aperture (i.e., a relatively small F-number) reference lens that satisfies the following inequality is required:
2NA greater than B/C. 
However, because of limitations on the size of the light beam diameter that enters into the reference lens, the following problems exist. If the lens components of the reference lens are all convex lens components and the incident light beam is converged by all these convex lens components, then every time refraction occurs at each lens component, the radius of curvature of the incident light beam wavefront, along with the light beam diameter, is gradually reduced, so that the radius of curvature of the light beam wavefront and the light beam diameter at the reference spherical surface becomes small.
If the subject spherical surface is a convex surface, the measurable subject spherical surface is limited to one where the radius of curvature is less than the radius of curvature of the reference spherical surface and where the diameter about the optical axis of the subject spherical surface is less than the diameter about the optical axis of the lens component that includes the reference spherical surface. Consequently, if the radius of curvature of the light beam wavefront and the diameter of the light beam emitted from the reference spherical surface are small, the shape and size of the subject spherical surface is so limited that it is difficult, if not impossible, to measure a subject spherical surface having a large radius of curvature and a large maximum diameter about the optical axis. Additionally, if as discussed above, the reference lens contains only lens components having positive refractive power, it is difficult to eliminate spherical aberration from the light image formed by interference.
In order to solve these problems, Japanese Laid-Open Patent Application 2000-346613 discloses a reference lens with a numerical aperture NA at the side of the subject spherical surface that is sufficiently large (NA=0.806) that, even if the subject spherical surface is a convex surface that has a large acceptance angle, it is possible to measure the surface accuracy of the entire subject spherical surface with a high degree of accuracy. However, the reference lens disclosed in the above-mentioned application is made of seven lens elements and is very large, with a maximum diameter about the optical axis of 480 mm. Problems of producing such a large lens, including technical problems of production and very high costs of production, as well as problems of practically handling such a large lens, make this reference lens impractical because of its size and weight. Therefore, further improvement is desirable.
The present invention relates to a reference lens for an interferometer with a large numerical aperture, having small aberrations (including small spherical aberrations), and with a reference spherical surface that has a relatively large radius of curvature and diameter about the optical axis, while still being light in weight and compact. These features enable highly accurate measurements to be obtained of the shape of a convex spherical surface having a large acceptance angle, a large radius of curvature, and a large diameter about the optical axis. The present invention relates specifically to a reference lens for a Fizeau interferometer which is suitable for highly accurate measurements of the shape of surfaces of optical components.