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A diffraction-limited system has imaging performance set primarily by diffraction rather than by optical aberrations.

The Ritchey–Chrétien reflector follows the same folded path as a Cassegrain reflector, but both the concave primary and convex secondary are hyperbolic. Their conic constants and separation are chosen to cancel third-order spherical aberration and coma. The focal plane is behind the perforated primary.

The absence of third-order coma gives a much more useful wide field than a classical Cassegrain reflector, making this design attractive for research imaging. It retains astigmatism and field curvature, so a large flat detector generally needs corrective optics; higher-order optical aberrations are not all removed. Both aspheric mirrors are more demanding to manufacture and align, and the usual secondary obstruction remains. The sketch illustrates the beam routing and mirror types; its conics are not an optimized aplanatic prescription.

Both methods reduce structured stellar residuals, rather than removing all noise. In angular differential imaging, changing atmospheric turbulence, imperfect adaptive optics, flexure and thermal drift change the point spread function between frames. The reference then fails to represent the instantaneous stellar field. Small sky rotation makes close companions contaminate their own reference, causing differential-imaging self-subtraction. Extended disks are especially susceptible; subtraction can alter shape as well as total flux. More images help independent photon shot noise, but do not necessarily average away correlated residuals.

Simultaneous spectral differential imaging avoids the time delay, but different channels have non-common-path wavefront errors. Chromatic optical aberrations, wavelength-dependent amplitude errors and out-of-pupil propagation prevent a perfect radial rescaling of speckle patterns. Filter throughput, detector calibration, image registration and atmospheric dispersion also leave subtraction residuals. Nearby bands align the stellar field better but give less positional diversity; wider separation gives more displacement but larger chromatic mismatch. A smooth-spectrum companion, or one too close for appreciable rescaled displacement, can undergo severe differential-imaging self-subtraction.

Artificial-companion injection through the complete processing pipeline and forward modelling can calibrate lost throughput and photometric or astrometric biases. They do not guarantee that every correlated residual is a real source. Independent epochs or spectral evidence remain valuable.

In the simple slit-image approximation, the projected slit width is $w=x{f}_{\mathrm{cam}}/f_{\mathrm{coll}}$. Equating this width to the separation $q\Delta \lambda$ of barely resolved features, using the grating dispersion, givesThis recovers the stated spectral resolving power under the assumption that the grating has unit anamorphic magnification.

For arbitrary distinct $\alpha$ and $\beta$, the anamorphic magnification of a grating must be included. At fixed wavelength, the grating equation gives $|d\beta /d\alpha |=\cos \alpha /\cos \beta$, so the slit image instead has width $w=x{f}_{\mathrm{cam}}\cos \alpha /(f_{\mathrm{coll}}\cos \beta )$. Thus the general slit-limited resolving power of a grating isThe two expressions agree in the Littrow configuration, $\alpha =\beta$. Without that condition or the unit-magnification approximation, the quoted $\cos \beta$ expression is not the general slit-limited result. Finite grating size, detector sampling, and optical aberrations can lower the actual resolution further.

$V_d$ is the Abbe number, a measure of inverse relative optical dispersion. Ordinary crown glasses have comparatively large $V_d$ and lower refractive index, while ordinary flint glasses have smaller $V_d$ and often higher index. The Abbe diagram below spans typical optical-glass values; the shaded family ranges are schematic, and the marked examples are catalogue data. Modern glass compositions broaden and overlap the simple crown/flint picture.

For a positive doublet with $V_{1d}>V_{2d}$, the preceding formulas require $f_{1d}>0$ and $f_{2d}<0$: a converging crown glass element and a diverging flint glass element. Their dispersion corrections cancel, while their net optical power is positive. A small difference in Abbe numbers requires large opposing component powers, which makes the design harder to correct for other optical aberrations.

The point spread function is the image of an unresolved point source. It describes blurring from diffraction, optical aberrations, and astronomical seeing.

A reflecting telescope forms an image using curved mirrors. Its primary and secondary shapes, spacing and aperture stop determine its optical aberrations, access to the focus, and obstruction.