Comparators and interferometry

Why it matters

Most production inspection does not measure absolute size; it compares a part against a master (a slip gauge stack or setting ring) and reads only the small difference. Comparators do this quickly with a magnification of hundreds or thousands, while interferometry uses the wavelength of light itself as a ruler to calibrate slip gauges, check flatness to fractions of a micrometre and verify machine-tool positioning.

Key ideas

Comparator principle. The instrument is set to zero on a master of known size; the part is then placed under the plunger and the deviation is read. The comparator need only be linear and repeatable over a small range, so it can be highly magnified. Magnification = indicated movement / actual plunger movement.

Types of comparator.

• Mechanical: dial indicator (rack, pinion and gear train), Johansson Mikrokator (twisted metal strip that rotates a pointer as it is stretched), Sigma comparator (knife-edge and gear sector). Simple and robust, but friction, inertia and backlash limit magnification to roughly a few thousand.
• Optical: a mechanical lever tilts a mirror; the reflected beam turns through twice the mirror tilt, giving high magnification with no moving pointer mass. Profile projectors (also called optical comparators) project an enlarged shadow of a part onto a screen for comparison with an overlay drawing.
• Electrical/electronic: the plunger moves the core of an LVDT (linear variable differential transformer) or an inductive bridge; the output is amplified electronically, so magnification can be switched and the reading can be logged and sent to SPC software.
• Pneumatic: compressed air at constant supply pressure flows through a control orifice and then a measuring jet. Changing the gap between jet and workpiece changes the back pressure (back-pressure type) or the flow (flow type, read on a rotameter). Non-contact, self-cleaning and ideal for bore diameter, ovality and taper. The back-pressure response is nearly linear only over a limited middle range of the pressure ratio, which is where the gauge is set to work.

Interference of light. Two waves from the same source recombine; where their path difference is a whole number of wavelengths they reinforce (bright band), and where it is an odd number of half-wavelengths they cancel (dark band). Monochromatic light (sodium about 589 nm, helium, cadmium, mercury-198, or a He–Ne laser at 632.8 nm) is needed so that bands are clear.

Optical flat. A transparent disc lapped flat to a few hundredths of a micrometre, laid on the surface under test at a slight angle to form an air wedge. Light reflected from the bottom of the flat and from the surface interferes. Because the light crosses the air gap twice, moving from one dark band to the next means the gap changes by λ/2.

• Straight, parallel, equally spaced fringes: the surface is flat (only tilted relative to the flat).
• Curved fringes: the surface is convex or concave; the curvature measured in fringe spacings, times λ/2, gives the deviation from flatness.
• Concentric rings: a spherical high or low spot.

Interferometers. The NPL flatness interferometer and the NPL gauge-length interferometer use collimated monochromatic light to check flatness and calibrate slip gauges absolutely. In a Michelson or laser interferometer a beam splitter sends light to a fixed reference reflector and a moving reflector; each fringe counted corresponds to a reflector movement of λ/2. Laser interferometers are used to calibrate CMMs and machine-tool slides over metres of travel, but need compensation for air temperature, pressure and humidity, which change the wavelength.

Formulas

Magnification M = output movement / input movement

• Mechanical levers in series: M = (l1/l2)·(l3/l4)…
• Optical lever with a mirror tilted by a plunger at arm length x and a scale at distance D: M = 2D / x (the reflected ray turns through twice the mirror angle).

h = n·λ/2

• h: height difference between two points, m; n: number of fringes (dark bands) between them; λ: wavelength of light, m. Applies to an optical flat in air with normal incidence.

d = N·λ/2

• d: displacement of the moving reflector in a Michelson/laser interferometer, m; N: fringes counted.

h = (λ/2)·(n/l)·L (comparing two slip gauges with an optical flat)

• n fringes seen across the test gauge of width l (mm); L: distance between the two gauges' measuring points (mm); h: height difference between the gauges.

Worked examples

Example 1 (standard): laser interferometer displacement.

Given: He–Ne laser, λ = 632.8 nm; the counter registers N = 25 000 fringes as the machine slide moves.

1. d = N·λ/2.
2. d = 25 000 × 632.8 × 10⁻⁹ / 2 = 7.91 × 10⁻³ m.

Slide displacement = 7.91 mm.

Example 2 (GATE level): comparing a slip gauge with a reference gauge.

Given: a reference gauge and a test gauge stand on a platen with their centres L = 40 mm apart, and an optical flat rests across both. With sodium light (λ = 0.5893 µm), n = 5 fringes are seen across the 10 mm width of the test gauge, and the flat is found to rise from the reference gauge towards the test gauge.

1. Fringe gradient over the test gauge: n/l = 5/10 = 0.5 fringe per mm.
2. Height change per fringe = λ/2 = 0.29465 µm.
3. Slope of the flat = 0.29465 × 0.5 = 0.1473 µm/mm.
4. Over the 40 mm separation: h = 0.1473 × 40 = 5.893 µm.

The test gauge is 5.89 µm larger than the reference gauge. (Whether it is larger or smaller is found by pressing on the flat and watching which way the fringes move, or from the direction of the wedge.)

Common mistakes

• Using h = n·λ instead of n·λ/2 for an optical flat; the light crosses the air gap twice.
• Counting bright bands and dark bands both as "fringes", doubling the answer. Count one kind only.
• Thinking straight fringes mean the flat is parallel to the surface. Straight fringes mean the surface is flat; parallelism would give no fringes at all (a uniform field).
• Forgetting the factor 2 in an optical lever: a mirror tilt of α turns the reflected beam by 2α.
• Using a comparator outside its linear range, or setting it on a master that is not the same nominal size as the part.
• Ignoring air refractive-index changes in long laser-interferometer measurements.

For GATE PI

Expect numericals on fringe counting with optical flats (height or flatness from n·λ/2), laser interferometer displacement, comparator magnification of lever and optical-lever systems, and conceptual questions on pneumatic gauging, LVDTs and what different fringe patterns mean. Practise unit conversion between nm, µm and mm, which is where most errors occur.

Quick check

1. An optical flat shows 8 dark bands across a surface under light of λ = 0.6 µm. What is the height difference?
2. What does a pattern of straight, equally spaced fringes indicate?
3. Name a comparator that does not touch the work.
4. A mirror is tilted by 0.001 rad. Through what angle does the reflected ray turn?

Answers: 1. 8 × 0.3 = 2.4 µm. 2. A flat surface slightly tilted to the optical flat. 3. Pneumatic (air) comparator. 4. 0.002 rad.