Detection of imprecise estimations for polarization-resolved second-harmonic generation microscopy

Abstract

Second-harmonic generation microscopy can provide estimation of some local molecule distribution properties. However, in order not to get erroneous conclusions, it is important to detect measurements with insufficient precision. Such a detection technique is developed considering an approximation of the ultimate precision provided by the Cramer-Rao bound. This method is characterized and a simple approximation of its detection and false alarm probabilities is developed.

Monitoring dynamic collagen reorganization during skin stretching with fast polarization‐resolved second harmonic generation imaging

“…In practice, the pixel dwell time and the number of incident polarization states cannot be easily decreased because they determine the signal‐to‐noise ratio in the P‐SHG images. Indeed, the accuracy of the determination of the collagen orientation and of other parameters extracted from P‐SHG images is related to the total number N of detected photons . This number N scales as the pixel dwell time multiplied by the number of incident polarization states.…”

Maturation of the Meniscal Collagen Structure Revealed by Polarization-Resolved and Directional Second Harmonic Generation Microscopy

“…A custom MatLab routine was then used to extract the relevant information from the P-SHG images. Briefly, a spatial FFT algorithm with respect to the angle θ is used to compute the Fourier transform (variable Ω) of the measured intensity 59 :where c.c. is the conjugated complex, and D the Dirac function (Fourier-Transform of cos θ).…”

“…Then, is directly in [−π/2, π/2] because the 2-arguments arctangent function atan2 casts its result in]−π, π]. For ϕ 4 , a simple arctangent must be used to avoid a wrong re-casting 59 , ϕ 4 which is then in [−π/8, π/8]. Putting , it has been shown that the combination ϕ = βϕ 2 + (1 − β)(ϕ 4 +mπ/4) gives the most accurate result 59 , with m in {−2, −1, 0, 1, 2} calculated to minimize the quantity 59 .…”

Monitoring aging‐associated structural alterations in Caenorhabditis elegans striated muscles via polarization‐dependent second‐harmonic generation measurements

“…. The way in which this uncertainty is avoided is based on the appropriate c 2 sign selection as described by Wasik et al [29]. In our case due to the fact that the expected anisotropy parameter is significantly smaller than the unit [8,14], the negative sign of c 2 has been chosen [9], whereas angle f c calculated via the built-in Matlab function atan2…”

“…In our case, due to the fact that a sample-based analysis has been followed, the precision of <B> and <f c > is determined as the SD of the corresponding values resulting from all the image pixels. It is worth to be mentioned that, recent studies present an alternative, new method where the precision of the calculated B and f c values can be estimated for each pixel [29,30].…”