DE4337857A1 - Evaluating the rotation of the polarisation plane of a measurement transducer - Google Patents

Abstract

Two optical signals are produced in a polarimetric arrangement consisting of two analysers. The optical signals are converted and evaluate by a device which determines the rotation of the polarisation plane. The inverse transfer function is used to determine the rotation angle of the plane of polarisation from the converted optical signals. Both converted optical signals are converted back using the inverse transfer function. The optical signals are acquired when the angular positions of the analysers wrt. the polarisation angle is symmetrical.

Description

The invention relates to a method and an arrangement for evaluating the rotation the polarization level of a transducer according to the preamble of the main claim. The The invention is based on a transducer of the type described in the Valente publication et al. (SPIE Vol. 1584 Fiber Optic and Laser Sensors IX, 1991).

Such transducers usually work on the basis of magneto-optical and / or electro-optical effect. The publication mentioned is a Faraday current transformers. The sensor of the cited transducer is one by one current-carrying conductor winding optical fiber. In the polarimetric Arrangement with a polarizer and two analyzers are two optical signals generated. These are converted and sent to an evaluation facility where the Rotation of the polarization plane is determined.

Transducers according to the generic term generate a signal whose intensity I according to the law of malus I = I₀ cos² (ϕ-α) depends on the measured variable proportional to the angle of rotation ϕ. The inverse transfer function must therefore be used to determine the measured value the arccos function. The common to all polarimetric sensors, However, the cos-shaped sensor characteristic is for large values of the angle of rotation ϕ (| ϕ | <± 45 °) ambiguous.

A very simple approach to solving this ambiguity is the counting method described in patent specification EP 0 125 329 B1. An output signal proportional to the measured variable is produced by counting the half-waves of the cos-shaped sensor characteristic. In principle, at least two channels with differently oriented analyzers are required so that the counting direction can be determined from the resulting phase-shifted intensity curves. While this method can be implemented in a simple manner, it only has a rough angular resolution. The counting method results in e.g. B. from the three channels with differently oriented analyzers a minimum angular resolution of only ϕ _min = 30 °.

In the method of Valente et al. in addition to a counting method with a Resolution of 180 ° intermediate values generated. There are the arccos values of one Photodetector signal and the sign of the second photodetector signal for conversion used. Thus, the process, for its technical implementation also digital com components, the arccos function with an expanded range of values.

Because of the quantization of the photodetector signal by the digital com Components for analog-digital (A / D) conversion (with 8 bits) only a limited number (256) of values, a read-only memory is used to implement the arccos function used. The result of the section-wise linearization is then at the data output of this read-only memory and forms (assuming a dual number representation) the low-order bits of the output signal proportional to the angle of rotation das through this and through the output of the counter (high-order bit).

A linear sensor characteristic would theoretically result in a uniform quantisie tion of this signal with a maximum angular resolution of 0.7 ° (180 ° / 2⁸). Because of however, the cos-shaped sensor characteristic results as a disadvantage of the method Valente et al. a strong dependency of the accuracy on the value of the measured variable and a reduced angular resolution for certain angles of rotation.

This is where the invention comes in to remedy the disadvantages mentioned.

The invention consists in the method specified in the feature of the main claim. Advantageous further developments and a circuit arrangement for carrying out the Procedures are shown in the subclaims.  

By using both signals x and y, the method cited by Valente et. al. a higher accuracy and thus a finer angular resolution at clearly less dependence on the measured variable.

According to current technology, photo detectors are used to convert the optical signals sets, but it is also conceivable to use other elements (non-electronic). Independent depending on the type of conversion, however, the changed optical ones are as follows Signals referred to as photodetector signals. The invention cannot only be used for Faraday Current transformers or related types are applied; it can be used anywhere be where there is an optical effect, in which measurement information directly into a Po larization plane rotation angle is transferred, or as for example with the Pockels effect possible, indirectly by converting a phase shift into a polarization plane rotation.

With the method according to the invention, the angular resolution of the Measured variable also covers the area between the photodetector signal and the measured variable (ϕ) due to the cos-shaped sensor characteristic be an ambiguous connection stands. In addition, the invention provides measures that ensure maximum accuracy ensure signal evaluation regardless of the value of the measured variable.

In a polarimetric arrangement according to the invention with two with respect to the ge rotated plane of polarization (ϕ = 0 °) (e.g. current = 0) symmetrically oriented analyzers (Analyzer angle + α and -α) the photo detector signals have the form:

U₁ = γ₁SI₀cos² (ϕ-α) = ½γ₁SI₀ (1 + cos (2 (ϕ-α)))

and

U₂ = γ₂SI₀cos² (ϕ + α) = ½γ₂SI₀ (1 + cos (2 (ϕ + α)))

with I₀ as the radiation intensity before the analyzers and the attenuation values γ₁, γ₂ the optical transmission links between analyzers and photodetectors and with the Steepness S of the photo amplifier.

In the case of the same attenuation on both transmission paths (γ₁ = γ₂ = γ), the photodetector signals U₁ and U₂ can be easily standardized with the following relationships to U _1N and U _2N :

U _1N = 2U₁ / (γ₁SI₀) -1 and U _2N = 2U₂ / (γ₂SI₀) -1 (Eq. 1)

or by using the previously written relationships:

U _1N = cos (2 (ϕ-α)) and U _2N = cos (2 (ϕ + α)) (Eq. 2).

The standardized signals U _1N and U _2N are then alternating signals which oscillate between the values 1 and -1.

For mutually different attenuation of the transmission paths (γ₁ ≠ γ₂), with which Use of optical fiber transmission links between analyzers and photo detectors are to be expected, other measures to generate the standardized signals required.

It is therefore proposed to normalize the analyzer signals U ₁ and U ₂ to their (positive) amplitudes U _1S and U _2S . For the technically important case of a sin-shaped rotation angle ϕ (t) = ϕ _S sinωt, the amplitude values are U _1S = γ₁SI₀ / k (ϕ _S ) and U _2S = γ₂SI₀ / k (ϕ _S ), with a normalization factor k (ϕ _S ) occurs. This is k (ϕ _S ) = 1 / cos² (ϕ _S - α) for ϕ _S <α and k (ϕ _S ) = k = 1 for ϕ _S <α.

For a large angle of rotation amplitude ϕ _S α, the normalization is complete

U _1N = 2U _x -1 and U _2N = 2U _y -1 with U _x = U₁ / U _1S and U _y = U₂ / U _2S (Eq. 3)

easy to implement. For smaller rotation angle amplitudes than the size of the analyzer angle (ϕs <α), however, there is a systematic deviation due to the dependence on the rotation angle amplitude ϕs, so that U _1N , U _2N according to Eq. 3 no longer the condition of Eq. 2 obey. Nevertheless, the signals U _1N = 2U _x -1 and U _2N = 2U _y -1 meet the requirement | U _1N | <1 or | U _2N | <1. A correction of the systematic deviation can be carried out because e.g. B. for ϕ (t) = 0 applies: U _x = U _y = k (ϕ _S ) cos²α. Due to the fixed analyzer angle α, this results in the normalization factor k (ϕ _S ). After this value has been buffered, it can be standardized by division, so that the dependence on the angle of rotation amplitude fTSt and thus the deviation from Eq. 2 is omitted: U _1N = 2U _x / k (ϕ _S ) -1 and U _2N = 2U _y / k (ϕ _S ) -1.

A circuitry solution is outlined in FIG. 1. The control signal for the intermediate storage of k results from the intersection points U _x = U _y , which correspond to the value present at ϕ = 0. For α <45 ° U _x = U _{y are} greater than 0.5 and for 45 ° <α <90 ° U _x = U _{y are} less than 0.5. This value k (ϕ) is provided by using a window comparator (FK) in connection with a sample (S) with an amplification factor v = 1 / cos²α.

A digital evaluation circuit according to the invention with evaluation of x and y alternating in sections is described in the block diagram of FIG. 3. In this embodiment, the standardized signals U _1N and U _{2N are} first converted into the time-discretized, digitized signals x and y using A / D converters. For optimal use of all bits of the A / D converter, it may be appropriate to adapt (amplify) the standardized signals U _1N and U _2N to the input voltage range of the A / D converter used. The signal processing is not affected by this, however, because the maximum and minimum of the digitized signals x and y are regarded as 1 and -1 (= range of definition of the arccos function) for the further considerations and thus the extreme values of the standardized signals U _1N and U Correspond to _2N .

A logic circuit L1 essentially generates an from the digital signals x and y Linearization signal L prepared in sections and control signals CLK (counting pulse) and U / D * (count direction bit) for a counter COU. The one corresponding to the angle of rotation ϕ Measured value S is composed (also in accordance with the method of Valente et. Al.) the output (count value Z) of the counter COU (high order bits) and the linearization worth L (least significant bits). This corresponds to when using the dual number representation Addition S = Z + L.

The analyzer angles α₁, α₂ can be freely selected in coordination with the evaluation method. In any case, however, the case α₁, α₂ = ± 45 ° with a phase shift of 180 ° be excluded between the photodetector signals because the determination of the Counting direction is not possible. The counting direction results from the phase shift between the clock signals T1 and T2 (see below); for α₁, α₂ = ± 45 ° this is  Phase shift always 180 ° and the absolute values of the slope of the signals are always equal.

The method for generating these signals is exemplified below with the associated circuit diagrams. The heart of the measurement signal evaluation is the so-called logic circuit L1 with the outputs L, CLK and U / D *. For the description of the processes, a symmetrical position of the analyzer angle is chosen without restricting the invention, a particularly favorable position being at α ₁ = + 225 ° and α ₂ = -22.5 °. Then there is the cheapest phase shift (90 °) between the photo detector signals. In this case, the photodetector signals behave complementarily with respect to their gradients, ie the gradient of one is maximum when that of the other is minimal (zero).

According to the invention, the photodetector signal is preferably the one with the current absolute larger slope used to calculate the linearization signal L.

The values of the inverse function (here arccos) are contained in a read-only memory EPR. The instantaneous values of the photodetector signals (or according to their normalized or Digitized signals x and y) are alternately on the read-only memory EPR given where the conversion taking into account the signals x / y * and T1 (see below) is made.

Since the slope of the cos-shaped signals is known for all angles of rotation ϕ, the Um switching condition derived directly from the instantaneous values of each of the signals (i.e. without Differentiation). To generate a changeover between the signals Switching signal x / y * the signals x and y or x and -y are compared and according to the Conditions x <y or x <-y linked by an exclusive OR: x / y * = (x <y) XOR (x <-y). The comparison takes place in comparators, at their outputs, depending on the conditions mentioned, the clock signals T1, T2 and CLK are pending. For x / y * = 1 points the photodetector signal x has the larger absolute slope, otherwise (x / y * = 0) has y the larger absolute slope. In the changeover points, the absolute amount is the Slopes of the photodetector signals equal: | dx / dϕ | = I dy / dϕ |. The formation of -y is in  the binary number representation by bitwise inverting of y. From the Determining the signal with the currently larger slope becomes a counting direction (Counting direction signal U / D *) determined. The time to generate a count pulse CLK (CLK = 1) is determined by the condition x = y. If the condition is not met, then CLK = 0.

The signals L, CLK and U / D * are determined by the following formulas:

L = ½arccos (x) + α for (x / y *) = 1 and (x <y) = 1
L = 90 ° -½arccos (x) + α for (x / y *) = 1 and (x <y) = 0
L = ½arccos (y) -α for (x / y *) = 0 and (x <y) = 1
L = 90 ° -½arccos (y) -α for (x / y *) = 0 and (x <y) = 0
CLK = (x ≡ y); U / D * = x / y *.

These equations initially apply to α <45 °. Find them for 45 ° <α ′ <90 ° Swap x and y and α = 90 ° -α ′ also use. All analyzer angles α ′ ′ <90 ° can be traced back to these basic intervals.

The value set of the linearization signal L can (as already mentioned) by tables (preferably in a read-only memory) or with a fast one Process computers can be calculated. With the digital linearization value L corresponds to the lowest value an angle of rotation of 0 ° and the highest value an angle of 90 °. Accordingly, the counter counts in 90 ° steps.

Based on the time course of the individual signals during a period of a sin-shaped rotation angle ϕ (t), FIG. 4 illustrates this method in detail.

Since only instantaneous values are evaluated with the logic circuit L1 or with a computer, no buffers are required to generate the signals L, CLK or U / DH *. In addition, since a limited number of input values are mapped to a likewise limited number of output values, it is preferably proposed to accommodate all of the above-mentioned processing steps in a single read-only memory with suitable content. Such an embodiment is feasible with common electronic means and methods; it is therefore not reproduced in detail, but is only indicated in FIG. 3 by the fact that the combination of the depicted components is represented in a read-only memory with the reference symbol L1.

By using read only memories with typically 16 address lines there is initially a limited resolution for the signals x and y of 8 bits each. Whether the resulting angular resolution meets the requirements for a measurement signal would have to be checked individually. When using larger semiconductor memory An improvement is conceivable.

There are deviations of the output signal (measured value S) from the actual angle of rotation ϕ available, which are caused by systematic errors. These are partly correct greedy. While the quantization error occurs in principle, an error deviation can occur ϕ-S are equalized according to the invention and brought to zero in a symmetrical position. The deviation arises from the cos characteristic; through it becomes a systematic Error generated depending on the slope. For troubleshooting, the Be calculation of the linearization value L according to the following condition, the value in each case the smallest deviation from the angle of rotation ϕ: L ′ = f (x, y) with | ϕ-L ′ | = min. (⇒ | ϕ-S | = min.).

The assignment L '= f (x, y) differs only slightly from the above Equations for the linearization value L, precisely around the correctable system matic error. This refinement of the method offers itself for realization also a variant with a logic circuit implemented in read-only memory. These Design is based on the simultaneous evaluation of x and y, d. H. it will not functionally switched between the photodetector signals.

A further advantageous embodiment can lead to a substantial simplification of the entire evaluation circuit by simplifying the standardization circuit. Since the digitization of U _{1N ′} = 2U _x -1 and U _{2N ′} = 2U _y -1 (corresponds to Eq. 3), the resulting pairs of values (x, y) ′ are unique for all rotation angle amplitudes ϕs - also for auchs <α can be assigned to an angle of rotation ϕ, the correction of the systematic deviation of Eq. 2 instead of the second standardization can also be implemented by adapting the read-only memory content. This eliminates the circuit LO outlined in dashed lines in FIG. 1 and, with maximum utilization of the photodetector signals, a minimal circuit configuration results (consisting of a peak value meter, divider, A / D converter, read-only memory and counter).

With regard to a practical implementation of the invention, there are still various Randbe conditions to be observed.

Scheduling

For the control signals of the counter COU it generally applies that the information about the counter direction U / D * by a time period T depending on the specifications of the meter when the counting pulse must arrive. To do this, it is proposed to delay the count impulse signal CLK by the small amount T and the intermediate storage of the counter signal U / D * on every positive edge of the CLK signal, so that:

CLK ′ = CLK (t-τ) and U / D * ′ = U / D * (↑ CLK).

In addition, linearization value L and count value Z are synchronized because from the temporal discretization or quantization of x or y when the counting pulse occurs A time offset occurs between the linearization value L and the count value Z, so that the measured value S is briefly incorrect. With the help of the delayed counting direction signal CLK 'and the DR signal usually provided by A / D converters (DR = Data Ready), which indicates the validity of the data, becomes a temporary storage the linearization value L and the count value Z delaying control pulse DR 'derived:

DR ′ = (CLK ′ * & DR).

Error detection and suppression

Due to the sensor characteristics, only certain combinations of x and y are possible at given analyzer angles. If a different pair of values (x, y) occurs (see Eq. 2), this indicates a misalignment of the analyzers or a malfunction in the electronic signals (e.g. noise). By using the read-only memory output ERR, this error can be displayed, for example, and / or by taking into account delayed control signals DR 'according to: DR' = (ERR * & CLK '* & DR) can be used to suppress the output signal. As a result, the last (valid) measured value S remains at the output until the next valid pair of values x, y occurs. In addition, the user is free to use the values stored in the read-only memory to give all pairs of values x, y to the output signal in accordance with the mapping rule L ′ = f (x, y) or to only pursue the valid or other strategies. A circuit sketched in Fig. 5 takes over the two functions described timing and error detection / suppression.

Offset correction

Due to the integrating property of the counter used in each case, the Count value Z and thus the measured value S generally superimposed an offset when the Measurement signal evaluation when measuring periodic quantities to one from the zero crossing different time is switched on. Measures to eliminate this offset are familiar to the expert. Correcting the offset directly on is particularly effective Counter. On the one hand, this can be done by determining the offset and subsequent subtraction or on the other hand by determining the zero crossing and resetting the counter happen at this point. In addition, if the counter consists of two individual counters Z1, Z2 then the sum of these two counters Z1 and Z2 provides an offset-free signal, if the counter Z1 in a maximum and the counter Z2 in the subsequent minimum the waveform is started. The following are available for determining the maxima or minima the negative or positive edges of the count direction bit U / D * '. With a sin för moderate waveform ϕ (t) = Φsin (ωt) applies:

Z1 (t) = Φsin (ωt) -Φ and Z2 (t) = Φsin (ωt) Φ,

so that the offset correction becomes: Z (t) = (Z1 (t) + Z2 (t)) / 2 = Φsin (ωt).

The embodiments of the invention are described in more detail in the figures. Show it

Fig. 1 is a normalizing circuit arrangement,

Fig. 2 shows a circuit arrangement according to the invention,

Fig. 3 shows the structure of the logic module L1 of Fig. 2,

Fig. 4 shows the pulse diagram,

Fig. 5 shows the structure of the block "timing / error suppression" and Fig. 6 shows the waveform and the error deviation.

An example of a normalization circuit arrangement is shown in FIG . With it, the photodetector signals U1, U2 originating from the optical signals (I1, I2) are normalized to their positive amplitudes U _1S , U _2S . DV21 fed. The amplitude value U _1S , U _2S is used as a divisor in the divider. The result is the signals U _x , U _y . These signals U _x , U _y are further processed in the circuit arrangement L0.

The elements Sample S with gain factor v = 1 / cos²α, window comparator FK and two dividers DV12, DV22 are used. After division by the normalization factor k (ϕ) and multiplication by 2, the signals in adders AD1, AD2 are reduced by the value 1; then the standardized photodetector signals U _1N , U _{2N are} present.

In FIG. 2, an embodiment of a circuit arrangement for evaluating the normalized photodetector signals U _{1N, 2N} U is shown. These are first converted into digital signals x, y in analog / digital converters A / D. The block L1 processes this signal in the manner previously described and supplies the signals L, CLK, U / D *, ERR. The temporary storage LA serves as a synchronizer.

U / D * 'and CLK' are delayed signals that can be generated in an additional circuit ZF, which is described in more detail in FIG. 5. DR is the data-ready signal of the A / D converter, or DR 'the correspondingly delayed signal. The additional circuit ZF takes over the two functions described timing and fault suppression. The counter output Z and the linearization signal L finally form the measured value S proportional to the angle of rotation ϕ.

In Fig. 3, the structure of the logic module L1 of Fig. 2 is shown. This calculates the linearization signal L and generates the counting pulses CLK and the counting direction bit U / D * for driving the counter COU. The digital signal x is fed to the comparator KO1 with the signal y and to the comparator KO2 with the inverted signal -y. The comparison process serves to determine the signal with the currently absolutely larger slope. The comparator outputs deliver the clock signals T1 and T2 according to the conditions x <y and x <-y. From the clock signals T1 and T2, the switchover signal x / y * is generated in an XOR gate, which indicates whether the signal x or the signal y has the absolutely greater slope and which controls the switchover between x and y by the multiplexer MUX. The signal with the absolutely greater slope is then switched through to the read-only memory EPR. The output of the read-only memory EPR forms the linearization signal L as a low-value component of the digital measured value S from the clock signal T1 and the changeover signal x / y *. The changeover signal x / y * simultaneously controls the counter as the counting direction bit U / D * COU on. The counting pulses CLK are generated by the output x = y. As already mentioned, the group of components in L1 can also be replaced by a read-only memory, which performs all the logic operations for calculating the signal L and for generating the signals CLK, U / D *, ERR using tables, and also eliminates the need for the standardization circuit can make.

Fig. 4 is an overview of the pulse and signal generated by the evaluation arrangement follow during a period of a sinusoidal rotation angle ϕ (t) = 500 ° sin2π 50 Hz · t with symmetrical position of the analyzers (α = 22.5 ° ). x and y are the two standardized and digitally converted measurement signals. The signal x or y located between the fixed values c and -c with dashed lines with c = ½√2 is used, which has the absolutely greater slope.

T1 and T2 are the clock signals, which according to the conditions x <y and x <-y from the Signa len x, y are generated. The count direction bit U / D * arises from the clock signals T1 and T2 and the counting pulses CLK result from the comparison x = y. The linearization signal L consists piece by piece of cos-shaped sections, which from the arc-cos relationship come. Z is a step-shaped signal which is supplied by the counter COU. The Addition of the signals L + Z results in the measured value S proportional to the angle of rotation ϕ.  

In FIG. 5, the structure of the device ZF from FIG. 2 is shown with the signal names used there in a particular embodiment. The ZF block is used for time control in the sense of a delay and error suppression. The counting pulse signal CLK reaches both the delay unit τ and the flip-flop FF. Behind the delay unit T is the delayed count signal CLK '.

In FIG. 6, the error deviation φ is φ-L between the rotation angle calculated and displayed in the off evaluation circuit linearization signal L as a function of φ the. The correctable systematic error has already been subtracted, so that the error deviation ϕ-L, which is independent of the angle of rotation ϕ and thus of the slopes of the signals x and y, results and is almost symmetrical. The fluctuations (linearity errors) around the zero line result from the step-like digital linearization signal L compared to the continuously rotating angle of rotation ϕ. In the Valente et al. the difference ϕ-L moves in the interval -3.5 ° to + 3.5 °. In FIG. 6 the cos-shaped sensor characteristic is represented by the quantities x, y.

Claims (17)

1.Procedure for evaluating the rotation of the polarization plane of a transducer on the basis of an optical effect causing the rotation of the polarization plane, with generation of two optical signals (I1, I2) in a polarimetric arrangement consisting of two analyzers, with conversion of the optical signals ( I1, I2) and with a device (L1) for evaluating the converted optical signals (U1, U2) and determining the rotation of the polarization plane, with the determination of the angle of rotation (ϕ) of the polarization plane from the converted optical signals (U1, U2) the inverse transfer function is used, characterized in that both converted optical signals (photodetector signals U1, U2) are converted with the inverse transfer function. 2. Method for the evaluation of measured values according to claim 1, characterized in that the optical signals (I1, I2) with a symmetrical angular position of the analyzers with respect to the polarizer angle (ϕ = 0). 3. Process for the evaluation of measured values according to claim 2, characterized in that the optical signals (I1, I2) at an angular position of the analyzers of α₁ = + 22.5 ° and α₂ = -22.5 ° can be obtained. 4. Method for the evaluation of measured values according to one of the preceding claims, since characterized in that attenuation-loaded photodetectors by transmission of measured values gnale (U1, U2) damping adjusted and / or standardized. 5. Process for the evaluation of measured values according to claim 4, characterized in that the photodetector signals (U1, U2) are normalized to their amplitudes (U1S, U2S).   6. The method for the evaluation of measured values according to claim 5, characterized in that a further standardization by division by a value k is carried out with k = U _x / cos²α or k = U _y / cos²α at the point Stelle = 0 ° and / or Places the integer multiple of ϕ = 180 °, so that the dependence on the amplitude of the measured variable (ϕ) is eliminated. 7. Method for the evaluation of measured values according to one of the preceding claims, since characterized in that the linearization value (L) and of the count value (Z) until it is used again by a time which is greater than the delay for the arrival of the counting pulse (CLK). 8. Method for the evaluation of measured values according to one of the preceding claims, since characterized in that when a pair of values of the processed signals occurs (x, y) that does not meet the condition x = cos (2 (ϕ-α)), y = cos (2 (ϕ + α)), the output of the current measured value (S) is suppressed and instead the previous measured value is issued. 9. Method for the evaluation of measured values according to one of the preceding claims, since characterized in that an offset of the processed signals (x, y) is determined and by Subtraction or by resetting the counter (COU) is corrected. 10. Method for the evaluation of measured values according to one of the preceding claims, characterized in that the photodetector signals (U1, U2) vary in sections can be converted using the inverse transfer function. 11. Method for the evaluation of measured values according to claim 10, characterized in that that at one position the analyzer angle according to the condition | α₁ - α₂ | ≠ 90 ° the The sections are changed so that each photodetector signal (U1, U2) is switched with the absolutely larger slope.   12. Circuit arrangement for performing the method according to one of claims 10 or 11, characterized in that both processed signals (x, y) are continuously fed to a comparator (KO1, KO2),
that the comparator (KO1, KO2) selects that of the processed signals (x, y) with the currently absolutely larger slope,
that the comparator (KO1, KO2) forms a clock signal (T1) with the condition x <y and a second clock signal (T2) with the condition x <-y,
that a changeover signal (x / y *) for controlling a changeover switch (MUX) is generated from the two clock signals (T1, T2) with an XOR operation,
that the argument [2 (ϕ-a), 2 (ϕ + a)] of the photodetector signal (x or y) selected by the switchover signal (x / y *) is calculated via the inverse function (arccos) and divided by 2 and in that Condition T1 = 0 the argument is inverted as an intermediate result and added to 90 °, that by adding or subtracting the analyzer angle (α) depending on the changeover signal (x / y *) the linearization value (L) is created,
that a counter (COU) is incremented by 1 (if counting direction bit U / D * = 1 and x = y) or the counter (COU) is decremented by 1 (if counting direction bit U / D * = 0 and x = y) and that the measured value (S) is formed from the addition of linearization value (L) and counter value (Z). 13. Circuit arrangement according to claim 12, characterized in that the evaluation Circuit arrangement is connected upstream of a circuit arrangement which the photodetectors signals (U1, U2) according to one of the methods described in claims 4 to 6 adjusted for damping and / or nomination.   14. Circuit arrangement according to one of the preceding claims 1 to 9 or 12 to 13, characterized in that the function values of the Linearization value (L), the counting pulses (CLK) and the counting direction pulses (U / D *) for all combinations of the processed signals (x, y) and a counter by 1 increased (if count direction bit U / D * = 1 and CLK = 1) or decreased by 1 becomes (if count direction bit U / D * = 0 and CLK = 1) and the measured value (S) from the Addition of linearization value (L) and counter value (Z) is formed. 15. Circuit arrangement according to claim 14, characterized in that instead of processed signals (x, y) which are standardized by digitizing the peak values Signals formed by photodetector signals (x, y) 'for addressing the read-only memory to be used. 16. Circuit arrangement according to one of claims 12 to 15, characterized in that the circuit arrangement is constructed from discrete components. 17. Circuit arrangement according to one of claims 12 or 13, or 16, characterized characterized in that the circuit arrangement is designed as a process computer.