# Thin Film Quarter-Wave AR Coating Calculator

> Source: https://netray.co/tools/thin-film-quarter-wave-coating-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Find the quarter-wave physical thickness and the reflectance at the design wavelength for a single-layer anti-reflection coating, compared with the bare surface.

## Category

industry-templates

## Industry

Photonics and Optics Manufacturing

## Audience

- Optical coating engineer
- Process engineer
- Optics quality engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Design wavelength

**Key:** lam

**Type:** number

**Default:** 550

**Min:** 200

**Max:** 12000

**Step:** 1

**Unit:** nm

#### Coating refractive index

**Key:** n1

**Type:** slider

**Default:** 1.38

**Min:** 1.1

**Max:** 2.6

**Step:** 0.01

**Help:** MgF2 is about 1.38 in the visible.

#### Substrate refractive index

**Key:** ns

**Type:** number

**Default:** 1.519

**Min:** 1

**Step:** 0.001

**Help:** BK7 is about 1.519 at 550 nm; fused silica about 1.46.

#### Incident medium index

**Key:** n0

**Type:** number

**Default:** 1

**Min:** 1

**Step:** 0.01

**Outputs:**

#### Quarter-wave physical thickness

**Key:** t

**Expr:** lam / (4 * n1)

**Format:** decimal

**Primary:** true

**Description:** nm. t = lambda / (4 n).

#### Bare surface reflectance

**Key:** r_bare

**Expr:** pow((n0 - ns) / (n0 + ns), 2) * 100

**Format:** percent

#### Coated reflectance at design wavelength

**Key:** r_ar

**Expr:** pow((n0 * ns - n1 * n1) / (n0 * ns + n1 * n1), 2) * 100

**Format:** percent

**Primary:** true

**Description:** Per surface, normal incidence.

#### Ideal coating index

**Key:** n_ideal

**Expr:** sqrt(n0 * ns)

**Format:** decimal

**Description:** Index giving zero reflectance at the design wavelength.

#### Transmission gain per surface

**Key:** gain

**Expr:** r_bare - r_ar

**Format:** percent

**Description:** Percentage points of light recovered.

**Chart:**

#### Coated reflectance (%) vs coating index

**Type:** line

**X:** n1

**From:** 1.1

**To:** 2.6

**Steps:** 40

**Series:**

- r_ar

**Disclaimer:** Lossless, non-dispersive single quarter-wave layer at normal incidence. Broadband and angle performance needs multilayer design software.

## Content

**Intro:** A single quarter-wave layer is the simplest anti-reflection coating and the baseline against which multilayer designs are compared. This calculator gives the thickness to deposit and the reflectance you should measure at the design wavelength.

**Sections:**

#### How to use the calculator

**Body:** Enter the design wavelength, the coating material index, the substrate index and the incident medium, usually air at 1.0. The thickness output is the physical thickness for a quarter-wave optical thickness, which is the target for a quartz crystal or optical monitor. The two reflectance outputs let you see how much a single layer recovers. The sweep chart plots reflectance against coating index so you can see how close available materials come to the ideal index.

**Bullets:**

- Use indices measured at the design wavelength, not a nominal catalog value.
- Run the tool for each substrate material in your lot, since glass type changes the ideal index.
- Remember the result is per surface; a lens has two.

#### The physics

**Body:** A film of optical thickness one quarter of the wavelength produces reflections from its two interfaces that are out of phase by half a wave. Complete cancellation requires equal amplitudes, which happens when the film index is the square root of the product of the incident and substrate indices. The residual reflectance with a quarter-wave film is ((n0 ns - n1^2) / (n0 ns + n1^2)) squared. Away from the design wavelength, reflectance rises, which is why multilayers are used for broadband.

#### Worked example

**Body:** On BK7 glass with an index of 1.519, a bare surface reflects about 4.3 percent. A quarter-wave of MgF2 at 550 nm is about 99.6 nm thick and reduces the residual to approximately 1.3 percent per surface. The ideal index would be 1.23, which no durable dense film provides, which is why two- and three-layer designs exist. Higher index substrates such as SF11 get better results with MgF2 since their ideal index is higher.

#### Common mistakes

**Body:** People often quote the physical thickness at normal incidence and then deposit onto steeply curved parts where the thickness varies across the surface. Another is neglecting that deposited films have lower packing density and index than bulk, shifting the result. Always correlate with a witness sample measured on a spectrophotometer, and record the monitor tooling factor and batch in your quality system with each coating lot.

**Cta:** If your coating lot records, witness sample data and rework history are scattered, Netray can help link them to your ERP lot traceability.

**Faq:**

#### What is QWOT?

**Answer:** Quarter-wave optical thickness means the product of physical thickness and refractive index equals one quarter of the design wavelength. It is the building block of most optical coatings and sets the wavelength of minimum reflectance.

#### Why not use a coating with the ideal index?

**Answer:** Few durable materials have an index near 1.23 for glass. MgF2 at 1.38 is the common compromise. Porous or sol-gel films can approach lower indices, but durability and environmental stability become concerns.

#### Does this work for infrared?

**Answer:** The same formulas apply with the right indices and wavelength. Thicknesses are larger, and IR materials like ZnSe or germanium need their own index values. Enter the wavelength in nm, for example 10600 for CO2 laser optics.

#### How does angle of incidence change things?

**Answer:** At non-normal incidence the optical path through the film changes and the reflectance becomes polarization dependent. This calculator is for normal incidence only; use thin-film software for angled use.

## Search terms

quarter wave coating thickness calculator, single layer ar coating calculator, mgf2 coating thickness, optical coating reflectance calculator, qwot thickness calculator, anti reflection coating index, fresnel reflection calculator, optical thin film calculator

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