15.5 Comparators & Interferometry

The Comparison Principle

A comparator does not measure absolute dimension. It is first set to a known standard — usually a stack of slip gauges — and thereafter indicates only the deviation of each workpiece from that standard. This distinction is fundamental and frequently examined.

The advantage is decisive in production inspection. Measuring a 50.00 mm shaft to one micrometre absolutely requires an instrument accurate over its whole 50 mm range. Measuring the same shaft as plus 3 micrometres from a 50 mm standard requires accuracy only over a range of a few tens of micrometres, which is enormously easier and cheaper to achieve.

Characteristics of a good comparator

Note the inherent trade-off: magnification and range are opposed. A comparator with 10,000 times magnification has a very small usable range, which is why several types exist for different duties.

Mechanical Comparators

Magnification is obtained by levers, gear trains, or a combination.

Dial indicator

The plunger carries a rack that drives a pinion, and a gear train amplifies the rotation to a pointer. Magnification is typically 100 to 1000 times, with readings to 0.01 mm or 0.002 mm. It is the most common shop-floor comparator, used with a stand for bench work and mounted on machines for run-out checking.

Sigma comparator

Uses a knife-edge and a cross-strip hinge in place of a pivot, eliminating friction and backlash. A forked arm and a thin metal band wrapped around a drum give the second stage of magnification. Magnification reaches around 5,000, with readings to 0.0002 mm.

Johansson Mikrokator

A thin twisted metal strip carries a very light glass pointer at its centre. Axial tension applied by the plunger causes the strip to untwist, rotating the pointer. Because the mechanism has almost no mass and no rubbing contact, response is fast and hysteresis is negligible. Magnification reaches about 5,000.

Optical Comparators

Optical systems use a light beam as a weightless lever, which has three advantages: no mass, no friction, and no wear. A small tilt of a mirror produces a large movement of the reflected spot on a distant scale.

A critical geometric fact: rotating a mirror through angle $\theta$ deviates the reflected ray through $2\theta$, so the optical system contributes a factor of two before any lever ratio is considered.

Zeiss Ultra-optimeter

A plunger tilts a mirror, and the reflected beam is projected onto a graduated screen after multiple reflections. Magnification reaches 10,000 to 15,000 times, among the highest of any comparator.

Optical projector (profile projector)

Rather than magnifying a displacement, this magnifies the whole profile of a small component, projecting its silhouette at 10, 20, 50 or 100 times onto a screen where it is compared against a drawn chart. It is the standard method for inspecting screw thread forms, gear tooth profiles and small complex parts, since it checks form and dimension simultaneously.

Pneumatic Comparators

Air at controlled pressure escapes through the clearance between a gauging jet and the workpiece surface. The clearance controls the flow, and the flow or the resulting back pressure indicates the dimension.

Why pneumatic gauging matters in production

• No physical contact, so soft, thin or highly finished surfaces are not marked.
• Magnification of 1,000 to 30,000 times is readily achieved.
• Bores are measured directly, including deep, blind and interrupted bores that a mechanical instrument cannot reach.
• The gauging head is remote from the display, so measurement is possible in awkward positions and inside machines.
• The air flow blows swarf and coolant away from the measuring zone, which is a genuine advantage on a production line.
• Several jets can measure taper, ovality and bell-mouth in one operation.

The limitation is that the workpiece surface must be reasonably smooth, since roughness affects the escaping air flow, and each gauge is dedicated to one nominal size.

Electrical and Electronic Comparators

A displacement is converted into an electrical signal, most commonly by an LVDT — Linear Variable Differential Transformer — in which a moving ferrite core alters the coupling between a primary and two opposed secondary coils. The output is linear over the working range, frictionless, and has effectively infinite resolution.

Advantages that matter industrially: the signal can be amplified electronically to any magnification, recorded and logged automatically, used for statistical process control, and fed to automatic sorting or in-process gauging that stops a grinding machine at size. Multiple transducers can be combined arithmetically, so a single readout can display, for example, the difference between two measurements.

Comparator Comparison

Interferometry

Interferometry measures length in terms of the wavelength of light, which is why it sits at the apex of the accuracy hierarchy. Since 1983 the metre has been defined in terms of the speed of light, and practical realisation of that definition is by interferometry using stabilised lasers.

The optical flat

An optical flat is a disc of glass or fused quartz with faces flat to a fraction of a wavelength. Placed on a workpiece surface, it forms a thin wedge of air. Light reflected from the underside of the flat interferes with light reflected from the workpiece, producing alternating dark and light bands called interference fringes.

The governing relation is that consecutive dark fringes correspond to an air gap change of half a wavelength:

$\Delta h = \frac{\lambda}{2}$

For the helium 587.6 nm line commonly used, each fringe represents about 0.294 micrometres. Height difference over a surface is therefore

$h = n\,\frac{\lambda}{2}$

where $n$ is the number of fringes counted.

Reading fringe patterns

The pattern is a contour map of the surface:

Distinguishing convex from concave requires pressing lightly at one edge of the flat and observing which way the fringes move — a practical technique rather than a purely optical deduction.

Worked example

An optical flat placed on a gauge block face shows 8 fringes across a 20 mm length, using light of wavelength 0.5 micrometres. The height variation is

$h = 8\times\frac{0.5}{2} = 2 \text{ micrometres}$

Slip gauge interferometers

The NPL flatness interferometer and the Pitter-NPL gauge interferometer are used to calibrate slip gauges against the wavelength of light. The gauge is wrung to a base plate, illuminated with monochromatic light, and the fractional fringe displacement between gauge face and base plate gives the deviation from nominal length. Using several wavelengths together resolves the ambiguity of whole fringe counts — the method of exact fractions.

Laser interferometry

A stabilised helium-neon laser at 632.8 nm, with a beam splitter and retroreflectors, measures displacement to a resolution of nanometres over distances of tens of metres. It is the standard method for calibrating machine tool axes and coordinate measuring machines, and for checking positional accuracy, repeatability and backlash of CNC slides. Environmental compensation for air temperature, pressure and humidity is essential, because these alter the refractive index of air and hence the effective wavelength.