6. Experiments

Sðη~Þ ¼

Eq. (34), <sup>∂</sup><sup>η</sup> ∂ai

122 Optical Interferometry

result of measuring the ai-th argument.

error of η determination does not exceed 1%.

Figure 6. Theoretical (---) and experimental dependences η(ux).

dences of η on the plate shift ux.

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

is the first derivative of function η by argument ai, calculated at point ~a1, …, ~am, ~ai is

×S<sup>2</sup> ð~ai

vuut <sup>Þ</sup>, (35)

∂η ∂ai � �<sup>2</sup>

where η~ is experimentally found value of η, aiði ¼ 1, …, mÞ are values Ai,<sup>j</sup> and Bi,<sup>j</sup> featuring

the result of measuring value ai, and Sð~aiÞ the mean square deviation of random errors in the

We performed the transformations by Eq. (35) and assessed the error of value η determination in a typical experiment. We selected the variant with 8-bit digitization of the radiation intensity averaging-out half the dynamic range, the minimum speckle size slightly exceeding the TV camera pixel size, and Sð~aiÞ ¼ 0:7. Calculations showed that value ∂η=∂ai featuring Eq. (35) consists of sum m of random 10-2-order values of different signs. The random sign value appears due to randomness of intensity deviation from the average value in the speckle field. In the model experiment, a reflecting rough object in the form of a metal plate was used, and value η varied due to its shift. For a 10 × 10-pixel fragment of the speckle image, we obtained that Sðη~Þ decreases steadily with increase of η in the range from 0.3 to 0.999, and the relative

Essentially, the calibration technique for the optical systems intended to determine the optical path dispersion value was developed in Ref. [29]. In this technique, batched random variations of the wave phase difference were set by means of shifting a 1-mm thick transparent plate. The plate shift ux was performed with a 0.12-μm pitch. The plate roughness was prechecked with a WYKO NT-1100 optical profilometre. Figure 6 shows experimental and theoretical depen-

Xm i
