A method of step height and plate thickness measurement

within the unambiguous range of two laser wavelength

interferometer

Naoyui Koyama

Michelson interferometer

Use two lasers simultaneously Laser a wavelength :λa Laser b wavelength :λb

Laser a and laser b do not interfere each other

Optical path length difference

Intensit

y

of in

terfe

rence

Optical path length difference

Intensit

y o

f in

terfe

rence

Example 1

λa/λb=11/13

λa

λb

λa+λb

Moire pattern

Intensity variation within “beat” 　 B is inverse of “beat” A

Intensity varies periodicallyA → B → A → B

Optical path length difference

Inte

nsit

y of

inte

rfe

renc

e A B A

Example 2

A B A

Intensity variation within “beat” B is inverse of “beat” A

λa=635nm λb=785nm

→

Modifications of Michelson interferometer

DETECTOR : single detector → 　　 CMOS(or CCD) detectorMIRROR : perpendicular to the reference beam → slightly inclined

No part of the instrument is mechanically movable, making possible precise measurements free of backlash. 　

Optical path length of reference beam of column ris w(s-r)(sin2θ ） longer than column s

CMOS detector

0

1

2

Intensity (arb. unit)

r s Column number

(a) Upper step surface

r s 0

1

2

Intensity (arb. unit)

Column number

(b) Lower step surface

Step height is (1/2)(s-r)w(sin2θ)

CMOS detector

How to measure thickness of a plate

No plate is placed in the pass of measurement beam, or infinitesimal thin plate is set at zero point of optical path length difference, both case get same intensity variation as Fig. 1.

How to measure thickness of a plate

Intensity variation is periodic, when infinitesimal thin plate is placed at , same intensity variation as placed at is seen (Fig. 1).

How to measure thickness of a plate

Measurement beam passed through the prism is reflected by the plate. 　 When the plate is placed appropriately, intensity variation is the same as Fig. 1. Intensity variation of measurement beam not pass through the prism is shifted as seen in Fig. 2. Thickness of the plate d is calculable from this shift.

An example instrument to measure intensity variation and corresponding optical path length difference.

How optical axes of two wavelength laser diode coincide with each other by prism.

Compensation plate

Two beams partially overlap each other.Two wavelength Michelson interferometer is usable as one wavelength Michelson interferometer simultaneously.

ReferencesN. Koyama, A method of step height measurement within the unambiguous range of two laser wavelengths interferometer, Optik, 126 (2015) 313-316.

All slides shown here can be seen in my website.N. Koyama, http://www12.plala.or.jp/sokkyo/prism.html