10. Phase-shift to improve interferometry Flashcards
Processing fringe maps
What is the traditional approach to this?
What are two disadvantages?
What is an advantage?
To count fringes and/ or plot & interpolate
Disadvantages
- slow and tedious
- difficult with low fringe density
Advantages
- Superb ability of brain and eye
Automating the manual process.
Early approaches used fringe thinning and counting
There was limited success due to (3 reasons)
- difficulties of finding edges and centres
- highly convoluted or broken fringes required operator input.
- optical noise caused catastrophic problems
Concept of phase shifting.
The origin of this is in photo elasticity with the use of compensation methods to improve birefringence measurement.
What does aim to improve?
Improve precision, convenience and usefulness of all varieties of interferometry
What is the basic concept of phase-shifting?(4 points)
- insert a device in one optical path to shift phase
- measure intensity
- repeat several times with incremental shifts
- deduce phase map from resulting data
Sketch interference of plane waves propagating along axes α1 and α2
Interference bands
What 4 things is this term dependent on:
incidence angles
wavelength
initial phases
position of observation
Simple interferometer theory
express inference of plane wave front in the simple ,
what are the IR & IO terms?
IR & IO are the irradiance of the reference and object beams
Practical phase-shifting
All techniques are based on temporal phase modulation:
a time dependent relative phase-shift between the object and reference beams
what is modulation caused by (4 reasons) ?
moving a mirror
tilting a glass plate
moving a grating
rotating a quarter waveplate or polariser
Phase-shifting apparatus
Sketch a schematic of a typical phase shifting system
this is most commonly achieved by moving a mirror using a PZT (peizo-electric transducer)
Phase-shifting Theory
what are the two approaches to this ?
What is the basic interference equation and how is it used ?:
phase-stepping: change phase by known amount between measurements
integration (bucket) technique: integrate intensity while phase is shifted
solve for three unknowns, IR, IO, and f; where f is the relative phase between IR and IO
Phase shifting techniques
briefly descripe the three-step technique
and
describe the four-step technique
3-step technique.
A phase shift is added.
The intensity (reference and object) is a function of x and y .
Thi is dependant on the relative phase shift + the phase shift that is added in (or by stepping the phase)
steping phase, measuring intensity - thi can be found
4-step method
a fourth step is added and the difference between each phase step is pi/2
we only need 3 intensity maps to solve the 3 unknowns, however by taking more data than we need , it can cancel out some errors.
Phase-shift techniques
briefly describe the carré technique…..
aka bucket technique/integral technique
Take intensity maps
in previous techniques the shift, z was known now assume unknown but constant value of zeta
Comparison of generic methods
Phase-stepping and integration methods give …….. results;
except for ….-………. phase-shift errors where …………. methods are superior
……. method is best in presence of phase-shift errors
……. …… method is best for eliminating 2nd & 3rd order detection non-linearities
same
non-linear
integration
Carré
Four step
(READ UP ON EXAMPLES ON MOLE - P.E And Projection Moiré)
If you manually count the fringes - what are you doing ?
You are limiting your data ,
you are only accounting for the data on the fringes , not between the fringes.
Hence you require phase-shifting techniques for full field mapping
Phase-stepping Summary
Phase-shifting or …….-……. allows
- ….-……..
- ………
- ………..
- ……… ………… of fringe patterns
Same principles may be applied to a range of experimental techniques
Powerful, modern method which makes experimental validation of … viable
phase-stepping
- full-field
- rapid
- accurate
- digital analysis of fringe patterns
Same principles may be applied to a range of experimental techniques
FE
