Precision Displacement Measurement via a Distance Measuring Interferometer (DMI)

Why DMI Is Needed

Important characteristics of ``International Technology Roadmap for Semiconductors: 2001'' published by the SIA.

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General System

Laser IF

Electronics

Receiver

DMI system is comprised of three parts:1. IF2. Laser3. Electronics

DMI History

Year Description DMI Resolution

1887 Michelson-Morley Experiment. Leads to Michelson interferometer.

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1902 Pieter Zeeman wins Nobel Prize for effects of magnetic fields on atomic spectra. Leads to Zeeman split laser.

1960 Bell Laboratories develop first HeNe laser

1964 Airborne Instrument Labs, Division Cutler Hammer, first commercial displacement IF

1965 Zeeman HeNe Laser (HP)

1968 Perkin-Elmer “Lasergage” homodyne IF

1970 Zeeman laser IF (HP) /16

1987 20 MHz Heterodyne, with 2-pass (Zygo) /512

~1996 Current electronics (HP/Zygo). /2048

Michelson Interferometer

Michelson-Morley experiment (c.a. 1887). Typical use of the Michelson interferometer is to compare a test optical surface against a

known high quality reference flat. The output of the measurement is a light fringe pattern viewed from a diffuse surface. These fringes are spatial fringes.

Michelson Interferometer, Using Polarized Light

Laser

I

Photodetector

Heterodyne

Single Axis Interferometer10706B Plane Mirror IF

Multiaxis IF10735A

Design ConsiderationsCNC Protective Covers

Design ConsiderationsSplit Frequency Limit on Velocity

cf

144.74 10 HzHeNef

7.5 MHz: Agilent

20 MHz: Zygosplitf

max 4splitf

V

| | | | | | | |0 5 10 15 20 25 30 35

Frequency (MHz)

For a four pass plane mirror IF.

Design ConsiderationsMiscellaneous

• Vacuum compatibility.• Low adjustability.• Beam size.• Metric vs. U.S. Customary.• CTE between parent structure and IF parts.• Peak-to-Valley (PV) wavefront per optic.• Remote Receiver fibers (bend radius).

DMI System ErrorsDeadpath & Environment

Deadpath: Difference in physical optical path between Reference and Measure.

L0

Therefore, in this example the deadpath is L=4L0. This is assuming that the air space between the PBS and the two quarter wave plates are equal.

DMI System ErrorsDeadpath & Environment

Edlen’s EquationMetrologia, Vol. 2, No. 2, Pg. 71, 1966

Air Temperature, T (°C) Barometric pressure, P (mmHg) Relative humidity, H (%) Gas composition. Typically not measured.

6

3 0.057621 (0.817 0.0133 ) 100.3836391 3.033 10

1 0.0036610TT

n P HeT

0c Ln

c OPL L

OPLn

nOPL OPL

n n

or , therefore

DMI System ErrorsAbbe Error

Abbe

,L

tanAbbe L Abbe error can be eliminated through with a measurement, and by knowing L.

1 2atany y

D

DMI System ErrorsCosine Error

•Reduced through proper alignment.•Part of the accuracy budget, and not the repeatability budget.•As an example, you can expect a 10706B to have a cosine error of 0.05 ppm (50 nm for a 1 m travel).

DMI System ErrorsErrors Summary

1. Make the ambient environment tightly-controlled and stable, and apply atmospheric compensation tools.

2. Minimize deadpath distances and Abbe offsets, and subtract in the processing.

3. Properly align the optics.

Summary

• DMI is currently the most accurate and sensitive linear translation measurement scheme. Additionally, it has a near limitless translation measurement bandwidth.• Relative, not absolute.• Noncontact.• Near coaxial measurement of translation axis.

• Resolution (Agilent 10897B electronics and two-pass IF): 1.2 nm.• Accuracy: ~2-3 nm.• Max. range: > 10 meters.• All 6 DOFs of a rigid body, are indirectly measurable.• Max. velocity (two-pass IF): 2 m/s.• Typical beam diameters: 3, 6 and 9 mm. 9mm is preferred.