Abstract
To simulate the effects of multiple-longitudinal modes and rapid fluctuations in center frequency, we use sinusoidal phase modulation and linewidth broadening, respectively. These effects allow us to degrade the temporal coherence of our master-oscillator laser, which we then use to conduct digital holography experiments. In turn, our results show that the coherence efficiency decreases quadratically with fringe visibility and that our measurements agree with our models to within 1.8% for sinusoidal phase modulation and 6.9% for linewidth broadening.
Highlights
Recent results show that digital holography (DH) is an enabling technology for tactical applications, such as deep-turbulence wavefront sensing[1,2,3] and long-range imaging.[4,5,6]
Recent experiments quantified the validity of this last statement in terms of system efficiencies.[8]. While these experiments showed that DH is robust against weak signals often encountered in tactical applications, they assumed the use of fully coherent laser sources when formulating closed-form expressions for the signal-to-noise ratio (SNR)
DH systems cannot, since the hologram interference fringes wash out when the path length differences between the signal and reference are greater than the coherence length of the MO laser
Summary
Recent results show that digital holography (DH) is an enabling technology for tactical applications, such as deep-turbulence wavefront sensing[1,2,3] and long-range imaging.[4,5,6] By flood illuminating a distant object and interfering the scattered signal with a local reference, we can reconstruct the amplitude and phase of the complex-optical field. This limit is primarily due to depolarization from rough surface scattering and the pixel modulation transfer function Other efficiencies, including those caused by excess reference and signal noise, can further degrade the fringe visibility. The S∕N and heterodyne energy is proportional to the square of the fringe visibility Note that this outcome is the same conclusion as Goodman for the amplitude interferometer.[20] For example, say the MO laser has a Lorentzian spectrum and the time delay, τ, between the reference and signal is equal to the coherence time, τc (as defined by Mandel[21]). The MO laser spectrum (i.e., the power spectral density) and γ are Fourier transform pairs via the Wiener–Khinchin theorem;[20] γ is a decaying exponential This example results in γ 1⁄4 0.368, ηc 1⁄4 13.5%, and the DH heterodyne energy and S∕N reduces by 86.5%. Operating a DH system at Δl ≥ lc is detrimental to the achievable SNR and limits the effective range to ≲lc∕2, assuming the signal travels much further to the object and back as compared to the reference
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