Coherent Backscattering from Multiple Scattering Systems - KOPS ...

5.1 Conservation of energy in coherent backscattering
the photodiodes. For such samples, the angular distribution of the backscattered intensity is
known to be proportional to the diffuson α d (θ) given in eqn. 2.14, as any deviations from the
incoherent background (i.e. the backscattering cone and the energy cutback) are too narrow
or too small to be detected by the setup.
The backscattering of the reference is also proportional to the incoming laser power P and
the total fraction of the backscattered intensity, the albedo A. The latter is reduced by energy
losses in the sample, mostly due to absorption of photonic energy, but also because of photon
leakage at the side and the rear surfaces.
For the calibration of the photodiodes only a relative power scale is needed, as one is merely
interested in compensating different gains of the diodes and their electronics. Therefore the
exact value of the albedo is not important, as long as it is independent of the inserted light
power. If however the albedos are known for sample and reference, one can derive an absolute
power scale for the diode signals.
Herein lies the misapprehension of [22, 23, 47], where the reference sample was also used to
determine the intensity level of the diffuson. As the different albedos of sample and reference
were neglected, this approach confuses relative and absolute power scale and therefore yields
slightly wrong results.
The photodiodes are calibrated by a series of measurements of the diode signals d θ at different
incoming light powers P, so that a relation between the diode signals and the light power
scattered in a certain direction θ can be derived. Previously used were relations like d θ ∝
α d (θ) · P [19], d θ ∝ cos θ · P, or even simply d θ ∝ P [22, 23, 47]. The latter however distort both
diffuson and cooperon for angles θ > 0, so that they can be used only if the backscattering
cone is comparatively narrow.
The effect of the different albedos of sample and reference can be incorporated in the calibration
function by the albedo mismatch b ℵ = A reference /A sample :
d θ ∝ α d (θ) · ℵ · P (5.2)
The albedo mismatch rescales the emitted intensity of the reference, so that the backscattering
of reference and sample is directly comparable.
The precision of the experimental result is determined by the precision of the reference measurements.
The order of the fitted polynomial must therefore be chosen such that the errors
are not artificially reduced. Based on the observations on fig. 5.1 we use 3rd order polynomials
to fit the data and obtain the calibration functions for the photodiodes.
5.1.2 Calculating the albedo
The albedo A of a multiple scattering sample is defined as the ratio of the (back-)scattered
light power P out and the inserted power P in . The albedo of a sample without any losses would
[b] ℵ = hebr. aleph
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