---
title: "Optical flat and flatness interferometer"
subject: "Metrology"
chapter: 8
key: "semester_3/metrology:flatness-interferometer-and-optical-flat"
source: https://www.bctengineer.com/q/semester_3/metrology/flatness-interferometer-and-optical-flat
site: BCT Engineering
---

# Optical flat and flatness interferometer

Metrology · Chapter 8: Interferometry

- Asked in: year not given, 8 marks
- Video: [Optical Flat](https://www.youtube.com/watch?v=tmFurBsknPc) — Dr Joji Thomas
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/metrology/flatness-interferometer-and-optical-flat
- Whole chapter: https://www.bctengineer.com/md/semester_3/metrology/chapter-8

## Question

Explain the interference of light and how an optical flat is used to test the flatness of a surface. Describe the NPL flatness interferometer.

## Short answer

An optical flat placed on a surface with a slight tilt forms an air wedge; monochromatic light produces interference fringes, each adjacent fringe indicating a height difference of λ/2. Straight parallel fringes denote flatness; curved fringes give error as (a/b)×(λ/2). The NPL flatness interferometer uses a mercury lamp, collimator, prism and tilting table to obtain sharp, bright fringes for precision flatness measurement.

## Answer

#### Interference of light
When two light waves of the same wavelength (coherent) meet, they add. If the path difference is a whole number of wavelengths ($n\lambda$) the waves reinforce (bright band); if it is an odd number of half wavelengths ($(2n+1)\lambda/2$) they cancel (dark band). A thin air wedge between two surfaces gives alternate dark and bright bands called **fringes**.

#### Optical flat
It is a disc of quartz or fused silica (or glass), optically polished flat to $0.05\ \mu$m or better. It is placed on the surface to be tested at a slight angle, forming a thin air wedge, and illuminated by monochromatic light (sodium or helium, $\lambda = 0.5893\ \mu$m). Light reflected from the lower face of the flat and from the work surface interferes. A dark fringe appears wherever the air gap is

$$
t = \frac{n\lambda}{2}
$$

so **adjacent fringes correspond to a height difference of $\lambda/2$** (about $0.3\ \mu$m).

| Fringe pattern | Surface |
|---|---|
| Straight, parallel, equally spaced | Perfectly flat |
| Curved (arcs) | Convex/concave; the bending of the fringe $\times\,\lambda/2$ is the error |
| Concentric rings | Not flat: spherical (convex or concave) |

If the fringes bend away from the line joining the edges by $a$, with spacing $b$, flatness error is $(a/b)(\lambda/2)$.

#### NPL flatness interferometer
It is used for testing the flatness of precision surfaces such as gauge blocks and measuring faces. A mercury-vapour lamp gives light that is passed through a filter and a slit, collimated by a lens, and reflected by a prism towards the optical flat resting on the test surface (on a table with three tilting screws). The reflected rays pass back through the prism to an eyepiece with a pinhole. The tilt screws adjust the wedge so that straight fringes appear; the pattern is observed and the error is calculated. It gives much sharper and brighter fringes than a simple optical flat in daylight.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Dark fringes appear when the path difference between two waves is:
   A. A whole number of wavelengths
   B. An odd number of half wavelengths
   C. Zero
   D. Twice the wavelength
   Answer: B. Path difference (2n+1) lambda/2 gives cancellation (dark band); n lambda gives reinforcement (bright). (Key point: Interference condition)

2. Adjacent fringes with an optical flat correspond to a height difference of:
   A. lambda
   B. lambda/4
   C. 2 lambda
   D. lambda/2
   Answer: D. A dark fringe appears where air gap t = n lambda/2, so adjacent fringes differ by lambda/2, about 0.3 micrometre. (Key point: Fringe height)

3. Straight, parallel, equally spaced fringes indicate that the surface is:
   A. Convex
   B. Concave
   C. Perfectly flat
   D. Spherical
   Answer: C. Straight equally spaced fringes mean a perfect air wedge, hence a flat surface; curved fringes show error. (Key point: Interpreting fringes)

4. If fringes bend by a with spacing b, the flatness error is:
   A. (a/b)(lambda/2)
   B. (b/a)(lambda/2)
   C. (a x b) lambda
   D. a lambda
   Answer: A. Flatness error = (a/b) x lambda/2. (Key point: Flatness error from curvature)

5. Why does an optical flat test use monochromatic light such as sodium?
   A. It heats the surface
   B. Coherent single wavelength gives clear alternate dark and bright fringes of known lambda
   C. It makes the flat quartz
   D. It removes the air wedge
   Answer: B. Monochromatic light of known wavelength produces sharp fringes whose spacing corresponds to lambda/2. (Key point: Monochromatic light)

## Related in Metrology

- [Fringe measurement of flatness error](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Ainterference-fringes-flatness-numerical) — Metrology, chapter 8

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