Application and Optimisation of the Spatial Phase Shifting ...

130 Comparison of noise in phase maps from TPS and SPS
number of samples and not α x ). The corresponding elliptical aperture shape was indicated in Fig. 5.1; its
area, and hence the object intensity it transmits, is three times that of the circular aperture.
I 0 I 1
I 2
I 0 I 1 I 2
Fig. 5.16: Adjustment of speckle width suitable for SPS with optimal light economy. Black bars: orientation and
spacing of carrier fringes, small squares: sensor pixels, irregular filled shapes: mean speckle size and
orientation; grey values of the shading on the speckles indicate their relative brightness.
The situation depicted on the left is the result of using a circular aperture: 2/3 of the coherence area are
superfluous for the phase calculation and the speckle field appears rather dark. But one can reduce the
speckle size from d sx d sy =33 d 2 p to d sx d sy =31 d 2 p , where d sx is the speckle width and d sy the speckle
height, to produce a brighter speckle image. On the right, an elliptical aperture generates speckles that are
just large enough to allow for phase calculation; the speckle intensity is greater by a factor of three,
indicated by the speckle outline in lighter grey. The question arises what improvement the change to
elliptic speckles will bring about: the plus in object light gives better M I or, optionally, allows to reduce
the gain of the camera amplifier; on the other hand, the non-circular average speckle shape causes the
measurement to become anisotropic with respect to displacement fringe orientations.
For TPS and SPS with circular and elliptic aperture, the behaviour of σ d was studied with the out-of-plane
set-up as in 5.1. To control the object illumination, I used a series of neutral density filters (D ∈ [1.0, 5.0])
directly behind MO1. The basic laser power density of O I =1.1 mW/cm² on the object was thus attenuated
to values between 110 and 0.01 µW/cm². The absolute value of sensor illumination could not be measured
accurately enough, but since we are still dealing with the comparison of TPS and SPS, the given power
scale will be sufficient for our purpose.
For each series, the chosen object intensities ranged from the first turning up of signal to the optimum
where further increase of the illumination power did not improve the measurements anymore. At the
lowest light level the interference was only just detectable in the speckle interferograms, * whereas the
speckle pattern alone was completely immersed in electronic noise. The reference light was always
adjusted so as to obtain a high average brightness of the interferograms, which decreases the contrast M I /I b
but maximises M I and thus reduces the noise somewhat. Even so, we have high noise and low M I due to
beam ratios exceeding 1000:1. This corresponds to R 190 grey levels and O0.2 grey levels, which of
course cannot be reliably measured; therefore the optical densities of the filter set served to determine
* Also, the light scattered from the object was detectable only by dark-accommodated eyes.