Instrumentation & Measurement Magazine 24-5 - 21

structures such as Gallium Arsenide (GaAs) [17], Indium
Nitride (InN) [18], Cadmium Telluride (CdTe) [19], monoclinic
Gallium Oxide (β-Ga2
O3) [20], and photorefractive
polymers [21]. The electric current is the result of the spatial
mismatch between the relatively stable space-charge electric
field distribution 
Ex , stored in the impurity centers
SC
of the photoconductive material, and the photo-excited carriers
distribution σ(x,t), which follows the instantaneous light
distribution, that is  
 x,  ,
t I xt . To observe the effect, the
Fig. 1. Block diagram of the proposed optoelectronic method for content level
measurement.
the container is excited with a light wooden stick by a gentle
and rapid impact. The laser beam is passed by a beam splitter
which generates a reference beam and a testing beam. The testing
beam hits the container and it is reflected by a small mirror
located on the surface container. This reflected beam impinges
onto the sensor, where it interferes with the reference beam.
The sensing element consists of a homodyne adaptive photorefractive
detector based on the so-called non-steady-state
photo-electromotive force (p-emf) effect [16]. The p-emf sensor
transforms the container vibrating pattern into an electric
signal proportional to the displacements of the target, which is
further processed to obtain the corresponding spectral content.
According to acoustic resonance principles, there is a direct relationship,
although nonlinear, between the spectral harmonic
information and the level of the container. That relationship
is learned by a neural network (NN) during a training stage,
by interrogating the container through a sequence of experiments
in which the level varies along the range from empty to
full. For that purpose, the numerical values of the several natural
frequencies are fed into a multilayer feed forward NN,
and configured as a nonlinear function approximator, which
performs a mapping of the vibrations to an output value. The
proposed method is a novel approach which takes advantage
of the optical system to detect the vibration pattern in non-contact
or non-invasive way and incorporates data analysis of the
spectral content using a NN-based technique.
The principle of operation of a photo-emf sensor is based
on the generation of an alternating electric current through
a short-circuited photoconductive material when it is illuminated
by an oscillating, spatially non-uniform light pattern.
The p-emf effect is typically observed in semiconductor
photoconductive sample is illuminated by an oscillating interference
pattern formed by two coherent plane waves, one
of which is phase-modulated at frequency f . The phase modulation
can be introduced either by a phase modulator placed
in the beam trajectory or reflecting the beam on a vibrating
mirror. The electrical current i generated by the adaptive photodetector
can be expressed as [16]:
i V CI AK F f ,
  
  
where A is the amplitude of the mirror vibration, I0
(1)
is the average
light intensity impinging on the adaptive photodetector,
K(α) and F(f) are functions that depend on the angle of the interference
beams (α) and the frequency of the mirror vibration,
respectively, and several electroptical constants contained
in C. An assumption made on the derivation of (1) is that
the amplitude of vibrations is smaller than the wavelength
of the used light (A « λ). These photodetectors are considered
adaptive in the sense that very efficiently they can detect
high-frequency, low-amplitude vibrations in the presence
of low-frequency, high-amplitude vibrations, such as those
produced by environmental perturbations, and can produce
an efficient signal with interfering beams containing irregular
wavefronts. These features are the result of the dynamic
properties on the formation of the space charge electric field
ESC

2 10 μm mW / Hz which is about
8
and the holographic processes involved in the formation
of the p-emf electrical current. The theoretical sensitivity of
adaptive photodetectors, that is, the minimal detected amplitude
of vibration is
one order of magnitude worse than the theoretical estimate for
an ideal photodiode. Adaptive photodetectors have been recently
employed for measuring vibrations in rough surfaces
[22], mechanical oscillations in transparent scattering objects
[23], focal length of a lens [24], elastic deformation and stresses
in transparent materials [25], and nanovibrations in general
[26], with potential applications in many industrial and scientific
fields such as biomedicine [27], material characterization,
Pros
Table 1 - Summary of p-emf sensor pros and cons specific to the proposed application
Cons
* Sensitivity below the detected signal with large margin
* The detection bandwidth can be adjusted by proper
selection of the sensor material
* Relaxed alignment
* Robust and low-cost device
August 2021
* Sensitivity is one order of magnitude worse than
conventional photodiodes
* They do not produce absolute measurements for
amplitude of vibrations, so calibration is needed
IEEE Instrumentation & Measurement Magazine
21
Instrumentation & Measurement Magazine 24-5

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