Fringe Contrast Fringe contrast - SPIEspie.org/samples/FG30.pdfFringe Contrast Fringe contrast is a...

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Fringe Contrast Fringe contrast is a measure of the interference quality. Good fringe contrast is needed to accurately measure interference signals. When the contrast is too low, the signal-to-noise ratio decreases. Fringe contrast is scaled 0 to 1, where 0 is no fringe contrast, and 1 is perfect fringe contrast. I FC ¼ I max I min I max þ I min ¼ I amp I mean Be sure to use a DC-coupled detector when measuring fringe contrast. Adjust the interferometer alignment to maximize the fringe contrast in the optical signal. Then, use electronic filtering and amplification to maximize the signal for analog-to-digital conversion. High DC offset leads to varying fringe con- trast for different sig- nal amplitudes. If the signal mean is half of the amplitude, then the maximum fringe contrast is observed. Use a high-pass filter (HPF) and an ampli- fier (G) to maximize the signal amplitude for analog-to-digital conversion (ADC). 12 Fundamentals of Light and Interference Field Guide to Displacement Measuring Interferometry

Transcript of Fringe Contrast Fringe contrast - SPIEspie.org/samples/FG30.pdfFringe Contrast Fringe contrast is a...

Fringe Contrast

Fringe contrast is a measure of the interference quality.Good fringe contrast is needed to accurately measureinterference signals. When the contrast is too low, thesignal-to-noise ratio decreases. Fringe contrast is scaled 0 to1,where 0 is no fringe contrast, and1 is perfect fringe contrast.

IFC ¼ Imax � Imin

Imax þ Imin¼ Iamp

Imean

Be sure to use a DC-coupled detector when measuringfringe contrast. Adjust the interferometer alignment tomaximize the fringe contrast in the optical signal. Then,use electronic filtering and amplification to maximize thesignal for analog-to-digital conversion.

High DC offset leadsto varying fringe con-trast for different sig-nal amplitudes.

If the signal mean ishalf of the amplitude,then the maximumfringe contrast isobserved.

Use a high-pass filter(HPF) and an ampli-fier (G) to maximizethe signal amplitudefor analog-to-digitalconversion (ADC).

12 Fundamentals of Light and Interference

Field Guide to Displacement Measuring Interferometry

Displacement from Phase Change

In DMI, narrow-linewidth sources are used, ensuring thatinterference occurs even when there are long optical pathdifferences (OPDs) between the measurement arm andreference arm. The reference arm of the interferometer isthe optical path that the light takes after the main splittingsurface until it interferes with the light from the measure-ment arm. Similarly, the measurement arm is the opticalpath of the light after the main splitting surface thattravels to and from the measurement target beforeinterfering with the light from the reference arm.

When light reflects N timesfrom a moving target, theoptical path is twice thephys-ical displacement, scaled bythe refractive index. Thus, Nis twice thenumber of passes:

zo ¼ nNzp

When the OPD is ml (form ¼ 0, 1, 2,:::), the armsconstructively interferebecause both opticalbeams are in phase. Asthe OPD changes to frac-

tions of wavelengths, the corresponding interferencephase changes proportionally. These phase changesare directly proportional to the change in OPD.

u ¼ 2pzol

¼ 2pnNzpl

¼ 2pnNzpfc

Since the measured phaseis a modulo-2p signal,the absolute phase isunknown, and only phasechanges can be measured.

Du ¼ 2pnNDzpl

! Dzp ¼ lDu

2pnN

Displacements larger thanl/nN result in a wrappedmeasurement phase signal.

20 Fundamentals of Light and Interference

Field Guide to Displacement Measuring Interferometry

Heterodyne Directional Sensitivity

Directional sensitivity in heterodyne interferometry isobtained based on the frequency difference between thereference interference signal and the measurement inter-ference signal. The reference interference signal (oroptical reference) is typically constant at a knownfrequency fs based on the heterodyne laser source. Whenthe measurement target is stationary, the measurementinterference signal is constant and equal to the opticalreference. When the measurement target moves, a Dopplershift occurs in the measurement interference signal,causing the frequency to increase or decrease.

In the Fourier spectrum, theoptical reference is fixed. Whenthe measurement signal has afrequency lower than the opti-cal reference, the target is mov-ing away from the interferome-ter because the signal isundergoing a negative Doppler

shift. Similarly, measurement signals with a higher frequencythan the optical reference undergo a positive Doppler shift.

Because the phase change is measured relative to a signalwith a defined frequency, there is no directional ambiguity.As long as the phase is correctly unwrapped or fringes arecounted, heterodyne interferometers are inherently sensi-tive to direction.

32 Basic Interferometry Systems

Field Guide to Displacement Measuring Interferometry

Beam Walkoff

PMIs are largely insensitive to small target mirror tip-and-tilt motion due to the retroreflector in the interferometer.Small mirror tip-and-tilt motions do lead to lateraldisplacements between measurement and reference armsin PMIs. This lateral displacement, or beam walkoff,reduces the achievable fringe contrast because a smalleroverlapping zone is created that generates the interferencesignal.

The amount of walkoff scales based on the distance znbetween the interferometer and the target. Even for smallrotations, the walkoff can be significant if the distance tothe target is large. For small angles, the walkoff is� 2Dw=zn, which discounts the additional walkoff that willoccur in the beamsplitter and retroreflector. Both tip andtilt will generate walkoff, so the total beam overlap shiftsby DRw.

DRw ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Dx2wyþ Dy2wx

q

In many cases, the interfering beams have a Gaussianprofile. Small walkoff changes cause the overlapping area,and thus the fringe contrast, to significantly decrease.

38 Interferometry System Characteristics

Field Guide to Displacement Measuring Interferometry

Time Interval Analysis

Time interval analysis is a relatively simple method tomeasure the phase in heterodyne interferometry. Itsorigins stem from when microprocessor options for fixed-or floating-point calculations were limited. Both interfer-ence signals are detected, converted to a voltage using atransimpedance amplifier, and then converted to a squarewave using a zero-crossing detector (ZCD). The twosquare waves then behave as digital 1-bit signals that canbe compared to a fast clock (CLK).

The timestamp triggered by zero crossing is then recordedusing two counters, one for the reference and one for themeasurement. During a specific measurement interval, thenumbers of zero crossings and timestamps are recorded.The number of displaced fringes is determined by thedifference in zero crossings between the measurement andreference signals. Fractions of a fringe can be interpolatedby analyzing the timing of the last two measurementcrossings and the last reference crossing.

u

2p¼ R�M þ Tm,i � Tr

Tm,i � Tm,ði�1Þ

� �

Time interval analysis advantages:

• Relatively simple electronics processing.

• No unwrapping algorithm needed.

Time interval analysis disadvantages:

• Jitter in signals can cause false zero crossings.

• Signals are essentially averaged over an interval.

50 Interferometry System Characteristics

Field Guide to Displacement Measuring Interferometry

Straightness Interferometer

The displacement interferometer can be reconfigured as astraightness interferometer to measure straightnesserrors. Straightness errors are lateral changes in theposition of a target in the directions mutually orthogonalto the translation direction.

The typical straightness interferometer uses a Wollastonprism and straightness optics at the interferometer andtarget. The Wollaston prism splits input light based onpolarization with a nominal separation angle as betweenbeams. The straightness optics then consists of two mirrorsconfigured in a 180-as-deg angle. If the straightness opticsdisplaces, both optical paths change equally. If thestraightness optics laterally shifts, one interferometerarm gets longer, while the other gets shorter. This opticalpath change is then detected and converted to straightness.

zp ¼ 2Dx sinas

2

� �

The output angle in the Wollaston prism is typically small,between 0.1 and 2 deg, leading to a straightness sensitivityof between ~0.005Dx and ~0.035 Dx.

Straightness interferometer advantage:

• Insensitive to displacement changes.

Straightness interferometer disadvantages:

• Low-sensitivity measurement, often dominated byrefractive index fluctuations.

• Large straightness optics needed for longer distances.

• Straightness reference determined by mirror flatnesssymmetry deviation amplified by 1/sensitivity.

58 Special Interferometer Configurations

Field Guide to Displacement Measuring Interferometry