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
λa
λa/λb=11/13
Intensity of interference
Example 1
λb
Intensity of interference
Optical path length difference
Intensity variation within “beat”
B is inverse of “beat” A
λa+λb
Intensity varies periodically
A → B → A → B
Intensity of interference
Optical path length difference
A
B
Optical path length difference
Moire
pattern
A
Example 2
λa=635nm
λb=785nm
A
B
A
Intensity variation within “beat” B is inverse of “beat” A
→
Modifications of Michelson interferometer
DETECTOR : single detector → CMOS(or CCD) detector
MIRROR : perpendicular to the reference beam → slightly inclined
No part of the instrument is mechanically movable, making possible
precise measurements free of backlash.
CMOS detector
Optical path length of reference beam of column r
is w(s-r)(sin2θ）longer than column s
Intensity (arb. unit)
2
1
0
r
s
Column number
(a) Upper step surface
Intensity (arb. unit)
CMOS detector
2
1
0
r
s
Column number
(b) Lower step surface
Step height is (1/2)(s-r)w(sin2θ)
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
intensity variation as placed at
is seen (Fig. 1).
, same
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.
References
N. 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