Far Field measurement in the focal plane of a lens : a cautionary note

TL;DR

This paper investigates how slight mispositioning of the CCD camera in a lens-based setup can cause unexpected narrowing of the far-field pattern, impacting experiments in optical wave turbulence and potentially leading to misinterpretation of phenomena like wave condensation.

Contribution

It reveals the sensitivity of far-field measurements to camera positioning errors and discusses their implications for optical turbulence experiments and data interpretation.

Findings

Tiny CCD mispositioning causes pattern narrowing instead of broadening.

Finite optical component sizes produce diffraction patterns similar to thermodynamic equilibrium distributions.

Misinterpretation risk of wave condensation due to measurement artifacts.

Abstract

We study theoretically the accuracy of the method based on the Fourier property of lenses that is commonly used for the far field measurement. We consider a simple optical setup in which the far-field intensity pattern of a light beam passing through a Kerr medium is recorded by a CCD camera located in the back focal plane of a thin lens. Using Fresnel diffraction formula and numerical computations, we investigate the influence of a slight longitudinal mispositioning of the CCD camera. Considering a coherent gaussian beam, we show that a tiny error in the position of the CCD camera can produce a narrowing of the transverse pattern instead of the anticipated and well-understood broadening. This phenomenon is robust enough to persist for incoherent beams strongly modified by the presence of noise. The existence of this phenomenon has important consequences for the design and the realization of experiments in the field of optical wave turbulence in which equilibrium spectra reached by incoherent waves can only be determined from a careful far-field analysis. In particular, the unexpected narrowing of the far field may be mistaken for the remarkable phenomenon of classical condensation of waves. Finally, we show that the finite-size of optical components used in experiments produces diffraction patterns having wings decaying in a way comparable to the Rayleigh-Jeans distribution reached by incoherent wave systems at thermodynamical equilibrium.