The Abbe sine condition is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It was formulated by Ernst Abbe in the context of microscopes.
The mathematical condition is as follows:
where the variables u, U are the angles (relative to the optic axis) of any two rays as they leave the object, and u’, U’ are the angles of the same rays where they reach the image plane (say, the film plane of a camera). For example, (u,u’) might represent a paraxial ray (i.e., a ray nearly parallel with the optic axis), and (U,U’') might represent a marginal ray (i.e., a ray with the largest angle admitted by the system aperture); the condition is general, however, and does not only apply to those rays.
Put in words, the sine of the output angle should be proportional to the sine of the input angle.
Read more about Abbe Sine Condition: Magnification and The Abbe Sine Condition
Famous quotes containing the words sine and/or condition:
“Faultless honesty is a sine qua non of business life. Not alone the honesty according to the moral code and the Bible. When I speak of honesty I refer to the small, hidden, evasive meannesses of our natures. I speak of the honesty of ourselves to ourselves.”
—Alice Foote MacDougall (1867–1945)
“Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.”
—Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)