OPTOELECTRONIC SYSTEM WITH SPLITTING OF A LIGHT BEAM FOR MEASURING ITS PLANAR DISPLACEMENTS

V. P. Tsipilev, V. I. Lukovnikov, P. I. Goskov

(Presented by the seminar of the AVT sector of the Scientific Research Institute of Nuclear Physics)

Known simple optoelectronic tracking systems with splitting of the light flux [1] determine only the sign of planar displacements of the light flux (up—down, left—right).

The modernized system described below makes it possible to determine directly the magnitude of these displacements (Fig. 1, a). When the light flux formed by optics 1 is displaced within the limits of its diameter, the four-sided mirror prism-analyzer 2 splits the flux into four parts, the illumination of which is determined by the magnitude and direction of the displacement. Reflected from mirrors 3, 4, 5, 6, the light portions are directed to photodetector 9. The presence of a modulating disk with a shaped cutout 7, rotated by electric motor 8, makes it possible to commutate the light fluxes in succession, as a result of which a sequence of pulses is taken from the output of the photodetector, the amplitude of these pulses being determined by the illumination of the light fluxes. Photosynchronizer 10, when the holes in the modulating disk are aligned with it, issues pulses \(a_1, a_2, a_3, a_4\) (Fig. 1, b), which, acting on the elec-

Fig. 1. Optoelectronic system with splitting of a light flux:
a) general view, b) schematic front view for zero spot displacements.

electronic part of system 11, distribute the signals from the photodetector over four channels. After amplification, the signals are summed according to the scheme [2]:

\[ \eta = (I_1 + I_2) - (I_3 + I_4), \]

\[ \xi = (I_1 + I_4) - (I_2 + I_3), \tag{1} \]

where \(I_1; I_2; I_3; I_4\) are photocurrents corresponding to the illuminances of the light parts \(E_1, E_2, E_3, E_4\) (Fig. 1, b).

For displacements of the luminous flux exceeding its diameter, i.e., for \(\eta, \xi > d\), the spot either passes entirely onto the face of the prism or “slides” along the edge. In the first case, one light spot will be located on the modulating disk in one of the shaded zones; in the second, there will be two in two adjacent zones (Fig. 1, b).

Figure 2 shows the path of the luminous flux. Conventionally, one face (the upper one) of the prism is shown; the mirror and disk correspond to the traces of the planes \(Q\) and \(R\).

Fig. 2. Toward the derivation of the geometrical relationships in the system

From analysis of Fig. 2 it follows that the displacements of the spot over the modulating disk are determined by the relations:

\[ dO_1 = 2H - L \tan 2\alpha + \eta/\cos 2\alpha, \]

\[ d'O'_1 = \xi . \tag{2} \]

Hence the minimum and maximum values of the displacements are determined by the expressions:

\[ (dO_1)_{\min} = 2H - L \tan 2\alpha = r_{\min}, \]

\[ (d'O'_1)_{\min} = 0, \]

\[ (dO_1)_{\max} = 2H - L \tan 2\alpha + h \tan \alpha/\cos 2\alpha = r_{\max}, \]

\[ (d'O'_1)_{\max} = h \tan \alpha . \tag{3} \]

Taking (3) into account, the dimensions of the zone on the disk in which the spot will move (Fig. 1, b) can be found as follows:

\[ \begin{gathered} l=2(h\tan\alpha+d),\\ \rho_{\max}=r_{\max}+d,\\ \rho_{\min}=r_{\min}+d. \end{gathered} \tag{4} \]

Analyzing expressions (2), one can see that the magnitude and sign of \(\eta\) and \(\xi\) can be determined from the polar coordinates \(r\) and \(\beta\) of the spot on the disk (Fig. 2) according to the following scheme:

\[ \begin{gathered} \eta=\cos 2\alpha\,(r\cos\beta-2H+L\tan^{2}2\alpha),\\ \xi=r\sin\beta. \end{gathered} \tag{5} \]

The quantity \(r\) can be determined from the width of the photocurrent pulse of the corresponding channel, if a cutout is formed on the disk with the following parameters:

\[ \begin{gathered} \rho_{\min}=r_{\min}+d,\\ \rho_{0}=(r_{\max}+d)/\sin(0.5\gamma_{0}),\\ \tan(0.5\gamma_{0})=l/2(r_{\max}+d). \end{gathered} \tag{6} \]

The profile of the curvilinear part of the cutout is an Archimedean spiral,

\[ r=\frac{\rho_{0}}{\gamma_{0}}\gamma. \]

It should be borne in mind that the system parameters \(H, L, h, \alpha\) must be selected so that \(\gamma_{0}\leq \frac{\pi}{4}\). Otherwise the cutout will overlap two adjacent zones. At a constant disk rotation speed, the value of \(\beta\) will be determined by the temporal position of the synchronizing pulse (for example, from hole \(a_{1}\), Fig. 2) and the leading edge of the pulse from the photosensitive element.

Fig. 3. Dependence of the photocurrent amplitude in channels 1 and 2 on horizontal displacements of the flux \(\xi\)

When designing the electronic part of the system, it should be borne in mind that it must ensure computation according to scheme (1) at

$\xi = 6\ \mathrm{mm}$

$\xi = 5\ \mathrm{mm}$

$\xi = 0$

$\xi = -5\ \mathrm{mm}$

$\xi = -6\ \mathrm{mm}$

Fig. 4. Oscillograms corresponding to the curves in Fig. 3. In each oscillogram, the upper curve is the signal of the time marker, $f = 400$ Hz; the middle curve is the shape of the photomultiplier photocurrent (left — channel 1, right — channel 2); the lower curve is the pulses from the photosynchronizer.

$\eta,\xi < d$ and according to scheme (5) for $\eta,\xi > d$; switching of schemes when passing from “small” $\eta$ and $\xi$ to “large” ones, and vice versa; making replacements in computation scheme (5) when passing to other channels, respectively, $\xi$ by $\eta$, $\eta$ by $-\xi$ (2nd channel); $\eta$ by $-\eta$, $\xi$ by $-\xi$ (3rd channel); $\eta$ by $\xi$, $\xi$ by $-\eta$ (4th channel).

The authors investigated an optoelectronic tracking system with separation of the light flux, which had the following parameters: $L = 250$ mm; $H = 130$ mm; $d = 6$ mm; $R_0 = 100$ mm. An FEU-36 was used as the photosensitive device. Since only horizontal $\xi$ displacements of the light spot were investigated, instead of a mirror pyramid a mirror wedge with an apex angle of $35^\circ$ and mirror dimensions of $100 \times 60$ mm was used.

The experimental results, presented in the oscillograms (Fig. 3) and the graph (Fig. 4), confirm the operability of such systems.

REFERENCES

1. Yu. G. Yakushenkov. Optical Systems of Photoelectric Devices. Nauka Publishing House, Moscow, 1966.

2. G. A. Medvedev, V. P. Tarasenko. Probabilistic Methods for Investigating Extremal Systems. Nauka Publishing House, Moscow, 1967.