Spectral speckle displacement in defocused and tilted imaging systems

Area of Science:

• Optics and Photonics
• Surface Metrology

Background:

• Speckle patterns reveal surface or light characteristics.
• Spectral Speckle Correlation (SSC) uses cross-correlation of speckle fields at different wavelengths to determine surface roughness.
• Defocus or object tilt introduces lateral speckle displacement, causing errors in SSC-based roughness measurements.

Purpose of the Study:

• To develop a model for determining lateral speckle displacement due to wavelength change in subjective speckle.
• To account for speckle displacement in defocused and tilted object measurements.
• To enable accurate surface roughness determination using SSC by correcting for displacement errors.

Main Methods:

• Modeling lateral speckle displacement for subjective speckle with varying wavelengths.
• Incorporating effects of object tilt and defocus into the speckle displacement model.
• Experimental validation of the developed model.

Main Results:

• A model was established to predict lateral speckle displacement for subjective speckle under defocus and tilt conditions.
• The model accurately estimates and corrects for speckle displacement across a range of wavelengths.
• Experimental validation demonstrated sub-pixel accuracy for object tilts up to ±7° and defocus distances up to ±25 mm.

Conclusions:

• The presented model effectively determines and corrects lateral speckle displacement in spectral speckle correlation.
• This work enhances the reliability of surface roughness measurements using SSC, especially for non-ideal sample geometries.
• The findings are applicable to diverse applications requiring precise surface characterization via optical metrology.