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In optics an imaging system must satisfy Herschel's condition to achieve perfect axial imaging along the optical axis. Herschel's condition implies the absence of spherical aberration in the system, although coma and astigmatism may still be present. Herschel's condition is closely related to the Abbe sine condition, which is the corresponding condition for achieving perfect imaging in a single transverse plane.

Suppose that an on-axis ray emanates from object space at axial position $$z$$, making an angle $$\theta$$ with the optical axis. After passing through the optical system, the same ray emerges in image space and intersects the axis at $$z'$$, making an angle $$\theta'$$. Let $$n$$ and $$n'$$ be the indices of refraction of the object and image space respectively. Then Herschel's condition is
 * $$\frac{n \sin \frac{\theta}{2}}{n' \sin \frac{\theta'}{2}} = M,$$

where $$M$$ is the lateral magnification of the imaging system.

Herschel's condition and the Abbe sine condition can be simultaneously satisfied only if $$\theta = \theta'$$, which implies that the lateral magnification must be $$M = \frac{n}{n'}$$.