Reflective Optics & Mirrors

1.1Why Mirrors Matter in Photonics

Mirrors are among the oldest and most fundamental components in optical systems. Every optical table in a modern photonics laboratory contains mirrors — for beam steering, focusing, cavity construction, and spectral selection. Unlike refractive elements, mirrors introduce no chromatic aberration because the law of reflection is independent of wavelength [1, 2]. A single mirror surface works from the deep ultraviolet through the far infrared without the dispersion that plagues lenses across broad spectral ranges.

This achromatic property alone makes mirrors indispensable for ultrafast laser systems, broadband spectroscopy, and any application spanning more than a narrow wavelength band. Mirrors also avoid substrate absorption losses entirely: the light never enters the bulk material. For high-power laser applications, this means less thermal load and higher damage thresholds compared to transmissive optics operating at equivalent power densities [4].

Reflective optics carry additional practical advantages. A mirror has only one optical surface to fabricate and characterize, compared to the two surfaces and bulk homogeneity requirements of a lens. Large-aperture mirrors are lighter and easier to support than equivalent lenses, which is why every major astronomical telescope — from Newton's first reflector to the James Webb Space Telescope — uses mirrors as primary light-gathering elements [1].

1.2Law of Reflection

The behavior of every mirror derives from a single principle: the angle of incidence equals the angle of reflection, measured from the surface normal [1, 2, 3].

Both angles are measured from the normal to the mirror surface at the point of incidence, not from the surface itself. The incident ray, the reflected ray, and the surface normal all lie in the same plane — the plane of incidence. This geometric simplicity is what makes mirrors analytically tractable and is the foundation for every equation that follows in this guide.

An important practical consequence: when a mirror is tilted by an angle Δθ, the reflected beam deviates by 2Δθ [1, 4]. This doubling effect makes mirrors sensitive alignment elements but also powerful beam-steering tools. A mirror mounted on a precision kinematic mount provides angular adjustment with twice the mechanical resolution.

For a deeper treatment of mount selection, adjustment sensitivity, and thermal drift, see the Optic Mounts comprehensive guide.

2.1Plane Mirrors

A plane mirror has a flat reflecting surface and produces a virtual image located the same distance behind the mirror as the object is in front of it. The image is laterally inverted, the same size as the object, and always virtual and upright [1, 2]. Plane mirrors introduce no optical power — they neither converge nor diverge light.

In photonics laboratories, plane mirrors serve as beam-steering elements, directing laser beams around an optical table along prescribed paths. A pair of plane mirrors can displace a beam laterally (periscope arrangement) or fold an optical path to fit within a confined space. In interferometry, plane mirrors serve as reference surfaces: the flatness of the mirror directly determines the measurement accuracy [6].

The critical specification for a plane mirror is surface flatness, typically expressed as a fraction of the test wavelength (e.g., λ/10 at 633 nm means the surface deviates from a perfect plane by no more than 63.3 nm peak-to-valley). For laser cavity mirrors, λ/10 or better is standard; for general beam steering, λ/4 may suffice [9, 10].

2.2Spherical Mirrors

Spherical mirrors have a reflecting surface shaped as a segment of a sphere. If the reflecting surface is on the inner (concave) side, the mirror converges light and has a positive focal length. If the reflecting surface is on the outer (convex) side, the mirror diverges light and has a negative focal length [1, 2, 3].

The radius of curvature R is the radius of the parent sphere. The focal length relates to R by:

This relationship holds in the paraxial approximation — that is, for rays close to the optical axis where sin θ ≈ θ. For concave mirrors, both R and f are positive by convention; for convex mirrors, both are negative [1, 2].

Spherical mirrors are the most widely manufactured curved mirrors because a spherical surface is the natural shape produced by conventional polishing processes — a tool rubbing against a workpiece with random strokes converges on a sphere. This manufacturing simplicity makes spherical mirrors significantly less expensive than aspheric alternatives [4, 7].

The limitation of spherical mirrors is spherical aberration: rays striking the mirror far from the axis focus at a different point than paraxial rays. This aberration becomes significant for fast mirrors (small f/#) and is the primary motivation for aspheric mirror designs [1, 4].

2.3Aspheric Mirrors

An aspheric mirror has a non-spherical reflecting surface described by a conic section or a general polynomial. The surface profile is characterized by the conic constant K (also called the Schwarzschild constant), which defines the shape [4, 5]:

where z is the surface sag (depth) at radial distance r, c = 1/R is the vertex curvature, r is the radial distance from the optical axis, and K is the conic constant (dimensionless).

The parabolic mirror (K = −1) is the most important aspheric mirror in photonics. A paraboloid brings all rays parallel to its axis to a single focal point without spherical aberration — a direct consequence of the geometric definition of a parabola as the locus of points equidistant from a focus and a directrix [1, 2]. This property makes parabolic mirrors essential for telescope primaries, laser beam collimators, and broadband focusing applications.

General aspheric surfaces add higher-order polynomial terms to the conic profile for additional aberration correction:

where α₁, α₂, α₃ are aspheric deformation coefficients. These additional terms are used in advanced optical design to correct multiple aberration orders simultaneously [4, 5].

3.1Mirror Equation

The mirror equation relates the object distance, image distance, and focal length for a spherical mirror under the paraxial approximation [1, 2, 3]:

where s is the object distance from the mirror vertex (positive if the object is in front of the mirror), s' is the image distance (positive if the image forms in front of the mirror, negative if behind), R is the radius of curvature (positive for concave, negative for convex), and f = R/2 is the focal length.

This equation is valid for both concave and convex mirrors, provided the sign convention is applied consistently. The standard convention in optics: distances measured in the direction of incoming light (toward the mirror) are positive for object distance; distances on the same side as the incoming light (in front of the mirror) are positive for image distance [1, 2].

The mirror equation assumes the paraxial approximation — it is exact only for rays infinitesimally close to the optical axis. For real systems with finite aperture, departures from this equation manifest as aberrations, particularly spherical aberration [1, 4].

3.2Magnification

The lateral (transverse) magnification describes the ratio of image height to object height [1, 2]:

A negative magnification indicates an inverted image; a positive magnification indicates an upright image. When |m| > 1 the image is magnified; when |m| < 1 it is diminished [1].

The longitudinal magnification — the ratio of image depth to object depth along the optical axis — is given by:

The negative sign indicates that longitudinal magnification always inverts depth: the front and back of an extended object swap positions in the image. The quadratic dependence on lateral magnification means longitudinal magnification is always larger in magnitude, producing depth distortion in magnified images [1, 2].

3.3Ray Tracing for Mirrors

Graphical ray tracing locates images by tracing any two of three principal rays from the top of an object [1, 2, 3]:

1. Parallel ray: A ray parallel to the optical axis reflects through the focal point (concave) or appears to diverge from the focal point (convex). 2. Focal ray: A ray passing through (or directed toward) the focal point reflects parallel to the optical axis. 3. Center-of-curvature ray: A ray directed toward the center of curvature strikes the mirror at normal incidence and reflects back on itself.

The intersection of any two of these rays (or their virtual extensions) locates the image. For a concave mirror with the object beyond the center of curvature, the image is real, inverted, and diminished. As the object approaches the focal point, the image moves to infinity. Inside the focal point, the image becomes virtual, upright, and magnified [1, 2].

4.1Focal Length from Radius of Curvature

The focal length of a spherical mirror is exactly half its radius of curvature, a result that follows from applying the law of reflection in the paraxial limit [1, 2]. This is one of the simplest and most important relationships in mirror optics:

For a concave mirror, R is positive and so is f, meaning the focal point lies in front of the mirror (on the same side as incoming light). For a convex mirror, R is negative and so is f, meaning the focal point lies behind the mirror (a virtual focus) [1, 2].

In practice, manufacturers specify either R or f on mirror datasheets. The radius of curvature is the directly measured quantity (using a test plate or interferometer against a reference sphere), while the focal length is the derived quantity used in optical design calculations [6, 10].

4.2f-Number and NA for Mirrors

The f-number (f/#) of a mirror describes the ratio of focal length to clear aperture diameter, just as it does for a lens [1, 4]:

The numerical aperture (NA) of a focusing mirror relates to the half-angle of the cone of light converging to (or diverging from) the focal point [1, 3]:

For a mirror in air, the relationship between f/# and NA is:

Lower f/# (faster mirrors) correspond to higher NA, larger cone angles, and tighter focused spots — but also greater susceptibility to aberrations. Mirrors faster than about f/2 require aspheric profiles to maintain diffraction-limited performance [4, 5].

5.1Spherical Aberration in Mirrors

Spherical aberration is the dominant on-axis aberration of spherical mirrors. It arises because the paraxial approximation (sin θ ≈ θ) breaks down for rays far from the optical axis: marginal rays — those striking the mirror edge — focus closer to the mirror than paraxial rays near the center [1, 2, 4].

where LSA is the axial distance between the marginal and paraxial focal points, h is the height of the marginal ray on the mirror surface, and R is the radius of curvature.

The transverse spherical aberration (TSA) — the radius of the blur circle at the paraxial focal plane — is related to LSA by [4]:

The circle of least confusion — the smallest cross-section of the converging beam — occurs at approximately 3/4 of the LSA distance from the paraxial focus, and its diameter is roughly 1/4 of the TSA blur at the paraxial focus [4, 5].

Expressing spherical aberration in terms of f-number provides an intuitive scaling rule:

This shows that LSA scales inversely with the square of the f-number. Doubling the f-number (e.g., going from f/2 to f/4) reduces LSA by a factor of four. This is why slow mirrors (f/8 and above) can use spherical surfaces with negligible aberration, while fast mirrors (f/2 and below) demand aspheric correction [4].

5.2Conic Sections and the General Asphere

The conic constant K determines which conic section the mirror profile follows, and each conic eliminates spherical aberration for a specific pair of conjugate points [4, 5]:

Sphere (K = 0): No specific aberration-free conjugate pair. SA present for all conjugates. Paraboloid (K = −1): Aberration-free for one conjugate at infinity (collimated light → focus). Ellipsoid (−1 < K < 0): Aberration-free for two specific finite conjugate points (the geometric foci of the ellipse). Hyperboloid (K < −1): Aberration-free for a virtual conjugate pair. Used as secondary mirrors in Cassegrain systems where the primary creates a virtual object for the secondary.

where e is the eccentricity of the conic section. For a parabola, e = 1, so K = −1. For a circle (sphere), e = 0, so K = 0 [4, 5].

5.3Off-Axis Parabolic Mirrors

An off-axis parabolic mirror (OAP) is a section cut from a larger parent paraboloid, displaced from the optical axis [9, 12]. The OAP retains the aberration-free focusing property of the parent parabola for on-axis collimated light, but the focal point is located to the side — away from the incoming beam path. This off-axis geometry provides unobstructed access to the focal region, which is essential for spectroscopy, fiber coupling, and detector placement [9].

OAP mirrors are specified by three parameters: the reflected focal length (RFL) — the distance from the center of the OAP surface to the focal point; the off-axis angle (OAA) — common values are 15°, 30°, 45°, and 90°; and the clear aperture diameter.

For a 90° OAP (the most common configuration), RFL = 2f_p:

OAP mirrors are extremely sensitive to angular alignment. Even milliradians of tilt between the incoming beam and the true optical axis introduce coma and astigmatism, rapidly degrading the focal spot [12]. Alignment typically requires an autocollimator or shear plate interferometer and is an iterative process of adjusting tip, tilt, and rotation.

6.1Metallic Coatings

The three metallic coatings used in the vast majority of photonics mirrors are aluminum (Al), silver (Ag), and gold (Au). Each has a characteristic reflectivity spectrum that determines its optimal wavelength range [8, 9, 10].

Aluminum is the most widely used mirror coating due to its broad spectral coverage and low cost. Bare aluminum reflects approximately 90–92% across the visible spectrum, with a reflectivity dip to about 87% near 800–900 nm. In the UV, aluminum maintains good reflectivity down to approximately 200 nm, making it the default choice for UV and broadband visible applications [8, 9]. Aluminum oxidizes rapidly in air, forming a thin Al₂O₃ layer that slightly degrades performance, so it is almost always used with a protective dielectric overcoat.

Silver has the highest reflectivity of any metal across the visible and near-infrared spectrum — approximately 97–99% from 450 nm through the mid-IR [8, 9]. Silver's weakness is its poor UV reflectivity (dropping below 90% at wavelengths shorter than ~400 nm) and its tendency to tarnish through reaction with sulfur compounds in the atmosphere. A protective overcoat is essential, and even protected silver has limited lifetime in high-humidity environments.

Gold provides excellent reflectivity (>97%) for wavelengths longer than about 650 nm, rising to >98% through the mid-IR and far-IR [8, 9]. Below 550 nm, gold reflectivity drops sharply, which produces its characteristic yellow color. Gold is chemically inert and does not tarnish, making it stable without a protective overcoat — an advantage for FTIR spectroscopy and other IR applications where overcoat absorption would be unacceptable. Gold on copper substrates is the standard mirror for high-power CO₂ laser systems at 10.6 μm.

6.2Protected and Enhanced Metallic Coatings

A bare metallic coating is mechanically fragile — it scratches easily and degrades through oxidation (aluminum) or tarnish (silver). The standard mitigation is a protective dielectric overcoat, typically a half-wave layer of SiO₂ or MgF₂ deposited directly over the metal film [8, 9].

Protected coatings add a single dielectric layer (or thin multilayer) that seals the metal surface against atmospheric degradation and allows cleaning with solvents (isopropanol, acetone). The protective layer has minimal impact on reflectivity at the design wavelength but may introduce minor spectral features — the aluminum reflectivity dip near 880 nm is partly enhanced by the SiO₂ overcoat [8].

Enhanced coatings use a more complex multilayer dielectric stack (typically 4–8 layers) over the metal to boost reflectivity in a targeted spectral band. Enhanced aluminum in the visible range achieves 93–96% reflectivity compared to 88–90% for protected aluminum. Enhanced silver for ultrafast laser applications achieves >98.5% from 600–1100 nm [8, 9].

The trade-off: every additional dielectric layer introduces stress to the coating stack, which can distort thin substrates and affect surface figure. Enhanced coatings also have greater polarization sensitivity than bare or protected metal — the multilayer structure splits s- and p-polarization reflectivities at non-normal incidence [9, 10].

6.3Dielectric High-Reflector Coatings

For applications requiring the absolute highest reflectivity — laser cavity mirrors, ring resonators, cavity ring-down spectroscopy — dielectric (all-dielectric) mirrors replace metallic coatings entirely. A dielectric mirror consists of alternating quarter-wave layers of high-index and low-index transparent materials. Constructive interference among the partially reflected waves produces reflectivity exceeding 99.9% at the design wavelength [1, 3, 8].

where n_H and n_L are the refractive indices of the high- and low-index layers, and N is the number of layer pairs. Common material pairs include TiO₂/SiO₂ (n_H ≈ 2.3, n_L ≈ 1.46) and Ta₂O₅/SiO₂. With N = 15–20 layer pairs of TiO₂/SiO₂, reflectivities exceeding 99.99% are achievable. Ion beam sputtering (IBS) produces the lowest-loss coatings, with scatter and absorption losses below 5 ppm [8, 10].

The bandwidth of a dielectric mirror depends on the refractive index contrast (n_H/n_L) and the number of layers. Higher contrast and more layers increase both peak reflectivity and bandwidth, but the mirror remains inherently narrowband compared to metallic coatings. Broadband dielectric mirrors use chirped or non-periodic layer designs to extend the high-reflectivity zone, but typically cannot match the octave-spanning coverage of a metallic mirror [1, 3].

Dielectric mirrors offer substantially higher laser damage thresholds than metallic mirrors — tens of J/cm² for nanosecond pulses compared to ~0.5 J/cm² for protected silver — because the dielectric materials absorb negligible light at the design wavelength [8, 10].

7.1Substrate Material Selection

The substrate is the structural body of the mirror — the material onto which the reflective coating is deposited. For a high-reflectivity front-surface mirror, the substrate's optical transmission is irrelevant; what matters is its mechanical stability, thermal behavior, polishability, and cost [9, 10].

The coefficient of thermal expansion (CTE) is often the most critical parameter. When a mirror absorbs even a small fraction of incident laser power, the substrate heats unevenly. A high CTE causes the surface to distort, shifting the focal point and degrading beam quality. For thermally demanding applications — high-power lasers, space telescopes, precision interferometry — substrates with CTE approaching zero are essential [10].

N-BK7 (Schott borosilicate crown glass) is the standard low-cost substrate for general-purpose mirrors. It polishes well, is widely available, and is adequate for applications without significant thermal loads. Its CTE of 7.1 × 10⁻⁶ /K means it deforms noticeably under moderate heating [9, 10].

UV fused silica (synthetic amorphous SiO₂) is the preferred substrate for high-power laser mirrors. Its low CTE (0.55 × 10⁻⁶ /K), high purity, and excellent UV transmission make it suitable for excimer laser optics and broadband systems. It also has a high laser damage threshold because its low absorption minimizes thermal effects [9, 10].

Zerodur (Schott glass-ceramic) achieves near-zero CTE through a carefully controlled crystallization process that balances positive-CTE glass and negative-CTE crystal phases. It is the standard substrate for precision reference flats, ring laser gyroscopes, and telescope primary mirrors where thermal stability over temperature swings is paramount [8, 10].

ULE (Corning Ultra-Low Expansion glass 7972) is a titania-silicate glass with even lower CTE than Zerodur under certain conditions. It is the substrate of choice for extreme thermal stability requirements such as space-based telescope mirrors and gravitational wave detector optics [10].

7.2Surface Specifications

Mirror surface quality is characterized by several complementary specifications [6, 9]:

Surface flatness (or figure) describes the deviation of the actual surface from the ideal prescribed shape. It is measured interferometrically and expressed as a fraction of the test wavelength, typically at 633 nm (HeNe). Common grades: λ/2 (~316 nm P-V) for commercial grade, λ/4 (~158 nm P-V) for standard precision, λ/10 (~63 nm P-V) for high precision and laser cavities, and λ/20 (~32 nm P-V) for reference-grade interferometry.

Surface quality (scratch-dig) quantifies cosmetic defects per MIL-PRF-13830B as two numbers (e.g., 40-20, 20-10, 10-5). The first number rates the worst scratch; the second rates the worst dig (pit). Lower numbers mean fewer and smaller defects. For laser mirrors, 20-10 or 10-5 is standard to minimize scatter [6, 9].

Surface roughness (RMS) describes high-spatial-frequency irregularities measured in angstroms (Å). Roughness determines scatter loss: higher roughness scatters more light out of the specular beam. For precision laser mirrors, roughness below 10 Å RMS is typical; ultra-low-loss cavity mirrors achieve <2 Å RMS [6, 10].

where TIS is the fractional power scattered, σ is the RMS surface roughness (same units as λ), and λ is the wavelength of light. For σ = 10 Å at λ = 633 nm: TIS = (4π × 1 nm / 633 nm)² ≈ 4 × 10⁻⁴, or about 0.04% scatter loss — acceptable for most applications. At shorter wavelengths, the same roughness produces proportionally more scatter [6].

8.1Off-Axis Aberrations

Beyond spherical aberration, mirror systems exhibit off-axis aberrations when imaging points away from the optical axis. These are the same Seidel aberrations that affect lens systems [1, 4, 5]:

Coma is the dominant off-axis aberration for parabolic mirrors. It produces a comet-shaped image blur that grows linearly with field angle. Coma arises because different annular zones of the mirror produce images at different lateral positions. A parabolic mirror eliminates spherical aberration on-axis but introduces severe coma for even modest field angles, which limits the useful field of view of Newtonian telescopes [1, 4].

Astigmatism produces two separated line foci (tangential and sagittal) for off-axis object points. The separation between these line foci increases with the square of the field angle. In a single concave mirror used at non-normal incidence — a common geometry in spectroscopy — astigmatism is often the limiting aberration [4, 5].

Field curvature causes the image of a flat object to form on a curved surface (the Petzval surface) rather than a flat plane. For a single mirror, the Petzval radius equals the mirror's radius of curvature. Multi-mirror systems can flatten the field by combining mirrors with opposite Petzval contributions [4, 5].

Distortion shifts the position of off-axis image points radially inward (pincushion) or outward (barrel) without blurring them. It is generally the least problematic mirror aberration in photonics, where on-axis or near-axis operation is most common [1, 4].

8.2Multi-Mirror Configurations

Telescope designers have developed several multi-mirror configurations to correct aberrations that a single mirror cannot eliminate. These configurations are also relevant to laboratory-scale reflective optical systems [1, 4, 7]:

Newtonian: A parabolic primary mirror with a flat secondary (diagonal) mirror to redirect the converging beam out the side of the tube. Free of spherical aberration on-axis but limited by coma off-axis. The simplest and most economical reflecting telescope design.

Cassegrain: A parabolic concave primary with a hyperbolic convex secondary. The secondary reflects light back through a hole in the primary, creating a compact design with a long effective focal length. Free of spherical aberration. Coma is present but reduced compared to a single parabolic mirror at equivalent f-number [1, 4].

Ritchey-Chrétien: A hyperbolic concave primary with a hyperbolic convex secondary. Eliminates both spherical aberration and coma (an aplanatic design), providing a wider useful field of view than the classical Cassegrain. The Hubble Space Telescope and most large ground-based research telescopes use this design. Manufacturing and testing hyperbolic surfaces is significantly more complex and costly than paraboloids [4, 7].

Schwarzschild: Two concentric spherical mirrors forming a catoptric (all-mirror) microscope objective. Used in UV and IR microscopy where lens materials are unavailable or have unacceptable absorption. Provides a moderate numerical aperture with zero chromatic aberration [4].

9.1Thermal Effects and High-Power Handling

When a mirror absorbs a fraction of incident laser power, the absorbed energy heats the substrate and coating. The resulting thermal gradient across the mirror thickness causes the reflecting surface to distort — a concave mirror under center-loaded heating develops additional curvature, effectively shortening its focal length [4, 10].

where δ is the peak-to-valley surface deformation, α is the coefficient of thermal expansion, P_abs is the absorbed power, D is the mirror diameter, κ is the thermal conductivity, and t is the mirror thickness. This is a first-order estimate; exact deformation depends on boundary conditions, beam spatial profile, and whether the mirror has reached thermal equilibrium [4].

9.2Beam Deviation and Alignment

A critical property of mirrors in alignment: any angular tilt of the mirror produces twice that angle of deviation in the reflected beam [1]:

This 2× multiplier applies to any plane or curved mirror and follows directly from the law of reflection. It means that mirror angular stability must be half the allowable beam pointing tolerance. In a laser system requiring ±10 μrad beam pointing stability, each steering mirror must be stable to ±5 μrad — a demanding requirement that influences mount selection (kinematic mounts, piezo-driven tip-tilt stages) and environmental isolation [4, 9].

For multi-mirror beam paths, angular errors accumulate. If a beam is steered by N mirrors in sequence, the worst-case beam deviation is the sum of all individual 2Δθ contributions. This makes minimizing the number of steering mirrors a design priority in precision optical systems [4].

9.3Ghost Reflections

A first-surface mirror reflects the beam from its front coating, as intended. However, a small fraction of light transmits through the coating (especially metallic coatings, which are partially transmitting) and reaches the back surface of the substrate, where it reflects again. This back-surface reflection exits the mirror as a weak secondary beam — a ghost reflection — displaced and angled slightly from the primary beam [9].

Ghost reflections are problematic in laser systems because they can damage downstream optics, create interference artifacts in measurements, or reach detectors as stray light. Mitigation strategies include:

Wedged substrates: A slight wedge angle (0.5–1°) between front and back surfaces separates the ghost beam from the primary beam, allowing it to be blocked by an aperture. AR coating on the back surface: Reduces the back-surface reflection, converting most transmitted light to a single-pass loss. Absorbing substrates: Using a substrate that absorbs at the operating wavelength attenuates the transmitted light before it reaches the back surface — common for high-power CO₂ laser mirrors on silicon or copper substrates [9, 10]. Thick substrates at non-normal incidence: Increasing the substrate thickness displaces the ghost beam laterally, making it easier to block.

Selecting the right mirror for a photonics application involves a systematic evaluation of wavelength, geometry, coating, substrate, surface quality, and mounting requirements. The following step-by-step workflow covers the key decision points [4, 9, 10]:

Step 1 — Define the wavelength range. This is the single most important parameter because it determines the coating choice. UV applications require aluminum (or UV-enhanced aluminum). Visible broadband systems work best with silver or enhanced aluminum. Near-IR and mid-IR systems use gold or silver. Laser-line applications may benefit from dielectric coatings for maximum reflectivity.

Step 2 — Choose the coating type. Use the spectral range, required reflectivity, damage threshold, and environmental conditions to select among metallic (Al, Ag, Au) and dielectric options. For pulsed lasers, check the damage threshold specification at the relevant pulse duration and wavelength.

Step 3 — Select the mirror geometry. Flat for beam steering. Spherical concave for general focusing (acceptable for f/4 and slower). Parabolic for diffraction-limited focusing or collimation of broadband light. OAP for off-axis configurations where access to the focal region is needed.

Step 4 — Specify the substrate material. N-BK7 for general purpose and cost-sensitive applications. Fused silica for UV, high-power, and precision systems. Zerodur or ULE for thermally critical applications requiring near-zero CTE.

Step 5 — Set surface quality requirements. Flatness: λ/4 for general beam steering, λ/10 for laser cavities and precision systems. Scratch-dig: 40-20 for general use, 20-10 for laser applications, 10-5 for intracavity or ultra-low-scatter requirements. Surface roughness: <20 Å RMS for standard laser mirrors, <5 Å for ultra-low-loss applications.

Step 6 — Determine the physical size and mounting. Select a diameter that provides adequate clear aperture (typically >85% of the physical diameter). Choose a standard size (12.7 mm, 25.4 mm, 50.8 mm) for compatibility with off-the-shelf mounts. Verify that the aspect ratio (diameter-to-thickness) provides adequate mechanical rigidity — a 6:1 ratio is typical for substrates up to 50 mm.

Step 7 — Verify compatibility. Check that the coating's damage threshold exceeds the application's peak fluence with adequate safety margin (typically 2–3×). Confirm that the substrate CTE is acceptable for the expected thermal environment. Ensure the selected mirror fits the available kinematic or fixed mount.