Читать книгу Optical Engineering Science - Stephen Rolt - Страница 19

This general description of an optical system is very economical in that the definition of conjugate points, focal planes, and principal planes provides sufficient information to determine the path of a ray in the image space, given the path of the ray in the object space. No assumptions are made about the internal workings of the optical system; it is merely a ‘black box’.

We see how input rays originating in the object space are mapped onto the image space for specific scenarios where the object is located at the input focal plan, the infinite conjugate, or the first principal plane. How can this be extended to determine the output path of any input ray? The general principle is set out in Figure 1.9. First, the input ray is traced from point P₁ as far as its intersection with the (first) principal plane at A₁. We know that this point, A₁, is conjugated with point A₂, lying at the same height at the second principal plane. This follows directly from the definition of principal planes. Second, we draw a dummy ray originating from the first focal point, f₁, but parallel to the input ray and trace it to where it intersects the first principal plane at B₁. We know that B₁ is conjugated with point B₂, lying at the same height on the second principal plane. Since this ray originated from the first focal point, its path must be parallel to the optical axis in image space and thus we can trace it as far as the second focal plane at P₂. Finally, since the object ray and dummy rays are parallel in object space, they must meet at the second focal plane in the image space. Therefore, we can trace the image ray to point P₂, providing a complete definition of the path of the ray in image space.

Figure 1.8 System focal lengths.

Figure 1.9 Tracing of arbitrary ray.