PCA-enhanced Speckle Interferometry with Bicubic Interpolation at the OAN-SPM México

Abstract We present an improved methodology for the reduction and analysis of speckle interferometry data, based on observations obtained with the 2.1 m telescope at the Observatorio Astronómico Nacional in Sierra San Pedro Mártir, México. Our approach combines Principal Component Analysis (PCA) filtering with bicubic interpolation to enhance both the signal-to-noise ratio and spatial resolution of the speckle data, while preserving the morphology of the autocorrelation functions. PCA is employed to suppress incoherent noise by reconstructing the speckle cube using only the dominant components, which correspond to consistent features across frames. Bicubic interpolation is then applied to refine the spatial sampling of the reconstructed images. Following these procedures, we apply a binary detection algorithm based on morphological filtering and adaptive threshold masking to identify companion candidates. The method was validated using a sample of 97 binary systems with well-determined orbital solutions. Our results show a substantial improvement in measurement precision: the average uncertainty in angular separation decreased from 10.3 to 4.5 mas, in position angle from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1</mml:mn> <mml:mover accent="true"> <mml:mi>.</mml:mi> <mml:mi>°</mml:mi> </mml:mover> <mml:mn>85</mml:mn> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0</mml:mn> <mml:mover accent="true"> <mml:mi>.</mml:mi> <mml:mi>°</mml:mi> </mml:mover> <mml:mn>91</mml:mn> </mml:math> , and in magnitude difference from 0.09 to 0.05 mag—corresponding to average improvements of 56.4%, 51.8%, and 42.6%, respectively. In tangential coordinates, the propagated uncertainty ρ σ θ exhibits a median reduction of 57.4%, commensurate with the radial uncertainty σ ρ . These results demonstrate the effectiveness of our technique for increasing the reliability of speckle interferometry measurements, particularly in the context of stellar multiplicity surveys and orbit calibration campaigns.