WO2012101631A2

WO2012101631A2 - Photodiode beam position and size sensor

Info

Publication number: WO2012101631A2
Application number: PCT/IL2012/000039
Authority: WO
Inventors: Eliyahu Bender
Original assignee: Ophir Optronics Ltd.
Priority date: 2011-01-24
Filing date: 2012-01-24
Publication date: 2012-08-02
Also published as: WO2012101631A3

Abstract

A photodiode detector for measuring beam power, impingement position and size. The detector has pairs of electrodes positioned at peripheral edges of a resistive surface of the detector, and an additional electrode positioned in the center of the resistive layer. The peripheral electrodes measure total power and beam position, and the central electrode additionally enables measurement of beam size. The voltage detected on the central electrode, when normalized for the power of the incident beam, provides a measure of the beam size, since the larger the beam, the less the Ohmic voltage developed on the electrode relative to the peripheral electrodes. The normalization to the power of the incident beam can be performed against the total sum of the currents collected from the peripheral electrodes, this summed current being proportional to the incident power. The voltage developed on the central electrode is proportional to the reciprocal of the beam diameter.

Description

PHOTODIODE BEAM POSITION AND SIZE SENSOR

FIELD OF THE INVENTION

The present invention relates to the field of optical power measurements performed by photodiodes, and especially to such power measurements which can also determine the size and position of the beam being measured.

BACKGROUND OF THE INVENTION

Photodiode Position Sensing Detectors (PSD) are known in the art, typically being silicon photodiodes of large area, typically 1 cm square or more, where at least one of the electrodes, front or back, is a sheet resistor instead of a good conductor. Such a PSD is shown in Fig. 1, which shows a prior art silicon detector that has sheet resistors 11, 12 on both front and back surfaces, that on the front 11 detecting the X position and that on the back 12 detecting the Y position. The PSD has four contacts, a, b, c and d. The incident beam impinging on the detector surface generates a current which is injected at that point of impingement. This current then divides itself into a current flow to the various contacts in accordance with the resistance to each contact, which is proportional to the distance of the point of impingement from each contact. As will be illustrated in Fig. 2B below, the injection point can be likened to the wiper arm of a potentiometer, and the current injected at this wiper arm divides according to the resistance between the wiper arm and each contact. Such a photodiode PSD thus uses potentiometric measurements on the sheet resistors in order to determine the position of impingement of an incident beam of light in the two orthogonal directions, X and Y. This light exposure generates a photocurrent at the point of impingement, which then divides amongst the pairs of electrodes according to the resistance between the point of photocurrent generation and the four electrodes. From the currents la, lb, Ic and Id in the electrodes, the location of the light spot is computed using the following equations. ^x— ¾r ^* . _j V ^~~ ½ " 7 : y

^Ib + Id ¼ + i_c

The constants kx and ky are simple scaling factors, which permit transformation of the current ratios into coordinates. An advantage of this process is the ability to perform continuous measurement of the light spot position with measuring rates up to over 100 kHz. The above type of 2-dimensional PSD is called "Duo-Lateral" because of the measurements in the two dimensions separated on the front and back of the detector. This enables use of a simple measurement system.

Reference is now made to Fig. 2A, which shows a pictorial representation of a Duo-Lateral type of PSD along with its schematic circuit representation in Fig. 2B. In the schematic circuit representation, Rp represent the potentiometric resistances across the resistive layer on the surface of the detector, (the two values of Rp assumed to be equal because of the symmetry of the device), P is the photoelectric current source, which is position dependent, and RSH is the shunt resistance between the front surface and back surface resistor sheets on the detector, D is the equivalent diode and Cj is the self capacitance of the device.

Because of the fact that the terminals on each side extend the width of the detector active area, there is dimensional symmetry and the response is uniform and linear. Because of this symmetry, the reading of the X-dimension sensing on the top terminals of the detector is not influenced by the Y position, and vice versa.

There also exist PSD's that measure position in both orthogonal directions using four contacts to a sheet resistor disposed on only one side of the detector. These are called Tetra-Lateral PSD's. Fig. 3 A is a pictorial representation of a prior art Tetra-Lateral type of PSD along with its schematic circuit representation shown in Fig. 3B.

Tetra-lateral position sensing detectors are manufactured with one single resistive layer 30 for both two dimensional measurements. They may feature a common cathode connected by the terminal marked BIAS, and four anodes, which is the implementation shown in Fig. 3A, or they could equally well be constructed with a common anode and four cathodes as shown in the remaining figures. The tetra-lateral detectors are advantageous when used in applications that require measurement over a wide spatial range.

The cathode connection may be a single common connection, and for two dimensional position sensing there are then four anode connections. The cathode current is proportional to the total incident light power. The sum of the current of the four anodes is equal to this cathode current, but is distributed among the four as a function of the beam position. In the tetra-lateral PSD, the dimensional symmetry of the duo-lateral PSD is lacking and the X-position signal is influenced by the Y position. This type of PSD needs to be calibrated for its non-uniformity and the result calculated by an appropriate algorithm.

The uniformity of the tetra-lateral PSD can be improved by shaping the electrodes on the four sides. This is referred to as the "Pincushion" configuration, and is illustrated in Fig. 4A, which is a pictorial representation of the Pincushion Configuration of the Tetra-Lateral type of PSD along with its schematic circuit representation in Fig. 4B.

Fig. 5 shows the construction of a common Planar diffused silicon photodiode. The anode is on the top where the light is incident. The cathode is on the bottom, and it can be coated with an opaque resistive metal layer electrode without interfering with the incoming light signal at the opposite face. ,

All of the above described prior art position sensing detectors are capable of determining the position of incidence of the center of an impinging beam. A photodetector, when properly calibrated, can be used as a power meter for laser beams having wavelengths to which the photodetector is sensitive. An important parameter regarding the laser beam itself is the beam size, as measured by any one of the parameters used in the art for such measurements. Photodiode power meters currently available are not able to provide a measure of this beam size. Beam size is an important parameter in applications involving the use of laser beams. Currently, a beam profiling instrument is generally required for performing such a measurement, and such a beam profiler is substantially more expensive for the user than a power meter.

There therefore exists a need for a beam position photodetector, which would also be able to determine the size of the impinging beam, and which would be of substantially lower cost than prior art beam size detectors.

The disclosures of each of the publications mentioned in this section and in other sections of the specification, are hereby incorporated by reference, each in its entirety. SUMMARY

There is described in this disclosure, an exemplary photodiode position sensing detector having pairs of electrodes positioned at the peripheral edges of a resistive surface of the detector, and further incorporating an additional electrode element positioned in the central portion of that surface of the detector, this additional electrode enabling measurement of beam size. The voltage detected on that central electrode, relative to the voltage of the peripheral electrodes, when normalized for the power of the incident beam, provides a measure of the beam size, since for a given beam power, the larger the beam, the less the Ohmic voltage developed on the electrode relative to the peripheral electrodes. This voltage arises from the current flowing within the resistive layer from the region of the central electrode to the peripheral electrodes, which are considered to be at ground potential. The normalization to the power of the incident beam can be performed against the total summed current flowing between all of the peripheral pairs of electrodes, and the photodiode electrode on the opposite side of the photodiode, this summed current being proportional to the total incident power. The direction of this current flow will, of course depend on whether the resistive layer and its associated electrodes - peripheral and central - are on the cathode surface or the anode surface of the device. For a square shaped detector, the pairs of electrodes may be disposed on the four opposite edges of the resistive layer of the detector surface. The additional central electrode is disposed on the same side as those peripheral electrodes, essentially in the center of the resistive surface layer. According to other exemplary implementations of such detectors, each of two pairs of peripheral electrodes can be arranged on opposite surfaces of the detector, one laterally opposing pair on each side, with resistive sheets or layers on both surfaces. The central size-determining electrode can then be positioned at the center of either surface, though the surface opposite the beam impingement surface has the obvious advantages of not interfering with the beam impingement and absorption.

A rigorous mathematical analysis shows that the voltage developed on the central electrode is closely proportional to the reciprocal of the beam diameter, over a large range of beam diameters for a given size detector chip. In order to avoid non-linear inaccuracies, the central electrode should be made as small as is possible, commensurate with the ease of manufacturing and connecting thereto. There is thus provided in accordance with a first exemplary implementation of the devices described in this disclosure, a a detector for measuring properties of an incident optical beam, the detector comprising:

(i) a planar photodiode detector element, having a resistive layer at one of its surfaces,

(ii) two pairs of electrodes disposed on the resistive layer, the pairs being positioned mutually orthogonally, and each electrode of each pair being disposed at opposite peripheral regions of the resistive layer, such that the position of an optical beam incident on the photodiode detector element can be determined from the ratio of the currents flowing between each of the electrodes of the pairs and a photodiode electrode on the opposite surface of the photodiode detector element, and

(iii) an additional electrode disposed in the central region of the resistive layer,

wherein the size of the incident optical beam can be determined for a given incident beam power, from the voltage measured on the additional electrode.

In such a detector, the voltage on the additional electrode may be measured relative to a common voltage on the pairs of electrodes. Furthermore, the power of the incident optical beam is then proportional to the sum of the currents flowing to or from at least all of the peripheral electrodes. The term "at least all of the peripheral electrodes", may further include the current flowing to or from the additional electrode.

In all of the above mentioned detectors, for an incident optical beam of predetermined power, the size should be proportional to the reciprocal of the voltage measured on the additional electrode.

Additionally, the pairs of electrodes on the resistive layer should advantageously be disposed on a surface of the planar detector element opposite to the impingement surface of the incident optical beam. These pairs of electrodes on the resistive layer may be strip electrodes disposed along edges of the planar photodiode detector element, or they may be discrete electrodes disposed at corners of the planar photodiode detector element. The additional electrode disposed in the central region of the resistive layer should have dimensions sufficiently smaller than the smallest beam intended to be measured that the accuracy of the measurement of beam size is not compromised. Another example implementation may involve a detector for measuring properties of an incident optical beam, the detector comprising:

(i) a planar photodiode detector element, having a resistive layer at each of its opposite surfaces,

(ii) a pair of electrodes disposed on each of the resistive layers, the pairs being disposed mutually orthogonally, and each electrode of each pair being disposed at opposite peripheral regions of its resistive layer, such that the position of an optical beam incident on the photodiode detector element can be determined from the ratios of the currents flowing between each of the electrodes of the pairs and the pair of electrodes on the opposite surface of the photodiode detector element, and

(iii) an additional electrode disposed in the central region of one of the resistive layers, wherein the size of the incident optical beam can be determined, for a given incident beam power, from the voltage measured on the additional electrode.

In such a detector, the voltage on the additional electrode is measured relative to a common voltage on the pair of electrodes disposed on the resistive layer on which the central electrode is situated. Furthermore, the power of the incident optical beam is proportional to the sum of the currents flowing to or from at least all of the peripheral electrodes. The term "at least all of the peripheral electrodes", may further include the current flowing to or from the additional electrode. In all of these last mentioned detectors, for an incident optical beam of predetermined power, the size is proportional to the reciprocal of the voltage measured on the additional electrode.

Additionally, the pair of electrodes disposed on the resistive layer on which the central electrode is situated should advantageously be disposed on a surface of the planar detector element opposite to the impingement surface of the incident optical beam. These pairs of electrodes on the resistive layer may be strip electrodes disposed along edges of the planar photodiode detector element, or they may be discrete electrodes disposed at corners of the planar photodiode detector element. The additional electrode disposed in the central region of the resistive layer should have dimensions sufficiently smaller than the beam being measured that the accuracy of the measurement of beam size is not compromised.

It is to be understood that the term resistive layer or resistive surface or the like, both as described and as claimed in this application, is intended to include any form of surface layer having the properties of a sheet resistor, whether that is achieved by means of a separate coating deposited onto or applied to a surface or surfaces of the planar photodiode element, or whether it is a layer built into the surface or surfaces of the semiconductor by means of doping or diffusion or any other method that can generate such an intrinsically resistive layer at the surface of the device.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be understood and appreciated more fully from the following detailed description, taken in conjunction with the drawings in which:

Fig.1 shows schematically a prior art position sensing detector with sheet resistors on both front and back surfaces;

Fig. 2A shows a pictorial representation of a prior art Duo-Lateral type of PSD;

Fig. 2B shows the schematic circuit representation of the PSD of Fig. 2A;

Fig. 3 A is a pictorial representation of a prior art Tetra-Lateral type of PSD; and

Fig. 3B shows its schematic circuit representation;

Fig. 4A is a pictorial representation of the Pincushion Configuration of a prior art Tetra-Lateral type of PSD; and

Fig. 4B is its schematic circuit representation;

Fig. 5 shows the construction of a common Planar diffused silicon photodiode, of the type that could be used for the PSD's described in this application;

Fig. 6 shows schematically the rear side of a Tetra-Lateral type of PSD constructed according to the methods of the present disclosure, with an additional terminal in the center, such that it becomes a position and size sensing detector (PSSD);

Fig. 7 shows a geometry for the cathode metallization for a PSSD of the type described in this application, having 4 dots in the corners for position sensing and a central dot for size measurement;

Fig. 8 illustrates the geometry of the cathode metallization for the detector of Fig. 7, using a smaller central dot for better resolution at small beam size and for minimizing the effect on the position measurement;

Fig. 9 shows the exemplary case of a circular section of a PSSD, showing an annulus of radius dr, as used for calculating the dependence of the detector output on beam size; Fig. 10 is a graph showing the voltage generated for such a PSSD as a function of beam diameter;

Fig. 11 shows the reciprocal graph to that of Fig. 10, showing a nearly linear function of the inverse voltage as a function of beam width; and

Fig. 12 is a schematic representation of a Duo-Lateral PSSD according to further implementations of the devices shown in this disclosure.

DETAILED DESCRIPTION

In this disclosure there is described a photodiode position sensing detector, further incorporating an additional detection element in the central portion of the detector to enable measurement of beam size. This is achieved by means of a terminal positioned in the center of the detector, and for tetra-lateral devices, on the same side as the four position sensing terminals of the PSD. This is illustrated in Fig. 6, which shows the back side of a Tetra-Lateral type of PSD with the four position sensing electrodes marked Cathodes 1 to 4, and such an additional terminal in the center, labeled Cathode 5.

The current is measured from each of the four outer terminals, which are maintained at the same potential which can be arbitrarily called ground. The currents measured are the current flows between these terminals and the conductive layer on the surface of the photodiode opposite that containing these terminals. The power of the laser beam is proportional to the sum of the four currents. The position of the laser beam is calculated from the four currents as is known in the prior art described hereinabove.

If the voltage of the center terminal is measured with respect to the ground voltage on the four outer electrodes, as defined above, and then this voltage is normalized relative to the power level of the impinging beam, which is proportional to the sum of the four measured currents above, then this normalized voltage is a function of the size of the laser beam. The beam size is approximately proportional to the reciprocal of this measured voltage divided by the total current, as will be shown hereinbelow. This detector is thus a position and size sensing detector - PSSD.

It is to be appreciated that the voltage of the center is measured with respect to the four outer electrodes at the edges of the sheet resistor on the same surface as the center electrode. The more concentrated the incident beam is relative to the center, the greater the Ohniic voltage drop across the resistive layer, from the center electrode to the peripheral electrodes. The Ohm's Law relationship of the voltage, current, and resistance in the resistive layer is thus being utilized for the measurement of the beam size. The anode could be any suitable voltage with respect to the four outer electrodes such that the total detector current is proportional to the incident light power.

For an accurate measurement of the size according to the foregoing, the laser beam should be generally centered on the detector. If the beam is not properly centered, then the voltage measured at the center will be reduced, giving an error to the measurement. If the amount of decentering is known, then it is possible to compensate the measurement by means of a suitable algorithm.

The actual geometry of the detector can be varied. For instance, the position measuring terminals do not need to be strips along the sides; they can be dots in the corners, as shown in Fig. 7, which shows a geometry for the cathode metallization for such a position and size sensing detector, having 4 dots in the corners for position sensing and a central dot for size measurement.

The size of the center terminal is an important parameter in terms of the size of the smallest beam that can be measured. It needs to be limited in size. If the size of the center terminal is large, then it limits the smallest beam size that can be measured. The terminal needs to be smaller than the beam in order for an accurate measurement of size to be obtained. The extent to which the terminal is smaller than the beam determines the accuracy with which the beam size can be measured, such that a quantitative criterion cannot be given. For most practical purposes, it is sufficient for the spot to be of the order of a few tens of percent, such as 20% to 30%, smaller than the smallest beam it is intended to measure for the size measurement to be accurate to within several percent. This terminal also disturbs the position measurement near the center if it is of significant size. Fig. 8 illustrates a geometry of the cathode metallization for a position and size sensing detector, using a smaller central dot for better resolution at small beam size and for minimizing the effect on the position measurement. Such a central, size determining electrode, can be also applied to the duo-lateral PSD, as will be described hereinbelow with respect to Fig. 12. In this case the behavior may be different in the X and Y dimensions.

It is possible to measure current from the center terminal as well as the four currents from the side terminals. This will force a change in the algorithm for calculating the position and size since if current is drawn from the center terminal, the total power measured is determined from the sum of these 5 currents.

As mentioned hereinabove, the size of the beam is approximately inversely proportional to the normalized voltage at the center electrode. In order to deduce the theoretical basis for the relationship between the center voltage and the beam size, reference is now made to Fig. 9, which shows the exemplary case of a circular section of a PSSD, showing an annulus of radius r and radial width dr, centered on the PSSD element, where the center terminal is located. The exemplary circularly symmetrical case is used only in order to simplify the mathematics, which can also be adapted to be applied to a detector having any shape. Besides the circular symmetry of the detector, for the purposes of this calculation, the laser beam is presumed to have a circularly symmetrical profile, and the beam is assumed to be centered on the detector.

The detector is laminar, one side being the cathode and the other side the anode. Consider that the side opposite the face on which the beam to be measured impinges, be it the cathode or be it the anode, has the resistive property of a sheet resistor of uniform sheet resistance p/sqUare. The sheet resistance is designated here in its commonly used units of Ohms/square. For the purpose of these calculations, it is assumed that the sheet resistance is ΙΟΟΟΩ/square, i.e. p = ΙΟΟΟΩ/square.

For the annular ring of the detector, the radial increment of resistance dR, or the resistance in the radial direction of the ring, is equal to the sheet resistance times the increment of radius and divided by the circumference of the ring. The radial "length" of the incremental ring is dr, while the "width" of the ring is its circumference 2πτ, such that the radial increment of resistance dR is given by: dR^-^-.dr

( 1 )

The resistance R from any radial position r to the electrical terminal at the outer edg detector, at radius a, is given by the integral of equation (1) from the radius r to a:

(2)

Upon performing the integration, the result obtained is:

R(r) := - --(ln(a) - ln(r)) (3)

2·π

Now considering a Gaussian beam of power PQ and beam width w, the annular radial increment of power becomes :

- 2-r² dP(r, w) :=P₀— ₂ e -dr

(4)

Since each element of the beam produces a photocurrent in the detector proportional to the power on that element, the increment due to the impinging beam power in equation (4) can be expressed in terms of the increment in photocurrent i₀:

- 2-r²

4-r 2

w

di(r, w) := i_Q- •e •dr

(5)

According to the principle of superposition as applied to linear systems, this being a linear system, the voltage generated at the center of the sheet resistor, or the potential between the center and the circular terminal at the outer edge of the detector is then the sum of the contributions of the voltages generated by all of the radial elements. This assumes, of course, that no current is extracted in the measurement of this voltage. According to

ons (5) and

Reference is now made to Fig. 10, which is a graph showing the voltage generated for such a detector as calculated using equation (7) for an incident Gaussian beam having a beam width w in the range of from 0.1mm to 5mm. The graph shows the effect of the beam size on the voltage generated for a constant power input beam, such that the total photocurrent collected from all of the terminals is constant. For this reason, the current does not feature in this graph.

Fig. 11 shows the reciprocal graph to that of Fig. 10, with a nearly linear function of the inverse voltage as a function of beam width, for beam widths of at least one tenth of the detector size.

A further exemplary implementation of the devices described in this disclosure, illustrated in fig. 12, is based on the duo-lateral type of PSD. In this type of PSD both the front surface and the back surface have the characteristic of a sheet resistor. The front surface has electrodes X and X' that measure incident beam position in the X dimension as has been explained above. The back surface has electrodes Y and Y' which measure beam position in the Y dimension. A fifth electrode marked V is added to the center of the back surface, and it adds the capability of measuring beam size, as has been explained above.

The fifth electrode, as well as the other four electrodes, is in electrical contact with its respective resistive surface layer or sheet resistor. This provides for measuring the voltage at the center of the resistive surface as has been explained above. The physical behavior and the mathematical explanation of how the measurement of this voltage enables the measurement of beam size are identical to that of the previously described embodiment based on the tetra-lateral PSD.

The fifth electrode is preferably placed on the back surface so as not to interfere with the beam incident on the detector. It could also be placed on the front surface, but in that case the area of the detector occupied by the electrode would be obscured. The fifth electrode is preferably a circular spot, and should advantageously be no more than about 0.3 mm diameter. If made much larger it becomes less accurate in measuring small beam sizes. If made much smaller is becomes difficult to manufacture and difficult to establish the electrical connection by means of a wire.

Of the three terminals on the back surface of the detector, the two on the periphery Y and Y' measure current. In so doing, they are maintained at the same voltage or electrical potential. If they were not maintained at the same voltage, the position measurement would not be accurate according to the explanation of the prior art duo-lateral PSD. Now the voltage measurement of the fifth electrode V is made with respect to the outside electrodes Y and Y'. In this connection it is noted that the electrodes on the front side X and X' need to be of equal voltage one to the other, however it is permitted for there to be a voltage difference between X and X' on one side and Y and Y' on the other side, since they have distinct measurement circuits.

It is appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and described hereinabove. Rather the scope of the present invention includes both combinations and subcombinations of various features described hereinabove as well as variations and modifications thereto which would occur to a person of skill in the art upon reading the above description and which are not in the prior art.

Claims

1. A detector for measuring properties of an incident optical beam, said detector comprising:

a planar photodiode detector element, having a resistive layer at one of its surfaces;

two pairs of electrodes disposed on said resistive layer, said pairs being positioned mutually orthogonally, and each electrode of each pair being disposed at opposite peripheral regions of said resistive layer, such that the position of an optical beam incident on said photodiode detector element can be determined from the ratio of the currents flowing between each of said electrodes of said pairs and a photodiode electrode on the opposite surface of said photodiode detector element; and

an additional electrode disposed in the central region of said resistive layer, wherein the size of said incident optical beam can be determined for a given incident beam power, from the voltage measured on said additional electrode.

2. A detector according to claim 1 wherein said voltage on said additional electrode is measured relative to a common voltage on said pairs of electrodes.

3. A detector according to either of the previous claims, wherein said power of said incident optical beam is proportional to the sum of the currents flowing to or from at least all of said peripheral electrodes.

4. A detector according to claim 3 wherein said sum of the currents flowing to or from at least all of said peripheral electrodes further includes the current flowing to or from said additional electrode.

5. A detector according to any of the previous claims, wherein, for an incident optical beam of predetermined power, said size is proportional to the reciprocal of said voltage measured on said additional electrode.

6. A detector according to any of the previous claims, wherein said pairs of electrodes on said resistive layer are disposed on a surface of said planar detector element opposite to the impingement surface of said incident optical beam.

7. A detector according to any of the previous claims, wherein said pairs of electrodes on said resistive layer comprise strip electrodes disposed along edges of said planar photodiode detector element.

8. A detector according to any of claims 1 to 6, wherein said pairs of electrodes on said resistive layer comprise discrete electrodes disposed at corners of said planar photodiode detector element.

9. A detector according to any of the previous claims, wherein said additional electrode disposed in the central region of said resistive layer has dimensions sufficiently smaller than the smallest beam intended to be measured that the accuracy of the measurement of beam size is not compromised.

10. A detector for measuring properties of an incident optical beam, said detector comprising:

a planar photodiode detector element, having a resistive layer at each of its opposite surfaces;

a pair of electrodes disposed on each of said resistive layers, said pairs being disposed mutually orthogonally, and each electrode of each pair being disposed at opposite peripheral regions of its resistive layer, such that the position of an optical beam incident on said photodiode detector element can be determined from the ratios of the currents flowing between each of said electrodes of said pairs and the pair of electrodes on the opposite surface of said photodiode detector element; and

an additional electrode disposed in the central region of one of said resistive layers,

wherein the size of said incident optical beam can be determined, for a given incident beam power, from the voltage measured on said additional electrode.

11. A detector according to claim 10 wherein said voltage on said additional electrode is measured relative to a common voltage on said pair of electrodes disposed on said resistive layer on which said central electrode is situated.

12. A detector according to either of claims 10 and 11, wherein said power of said incident optical beam is proportional to the sum of the currents flowing to or from at least all of said peripheral electrodes.

13. A detector according to claim 12 wherein said sum of the currents flowing to or from at least all of said peripheral electrodes further includes the current flowing to or from said additional electrode.

14. A detector according to any of claims 10 to 13, wherein, for an incident optical beam of predetermined power, said size is proportional to the reciprocal of said voltage measured on said additional electrode.

15. A detector according to any of claims 10 to 14, wherein said pair of electrodes disposed on said resistive layer on which said central electrode is situated is disposed on a surface of said planar detector element opposite to the impingement surface of said incident optical beam.

16. A detector according to any of claims 10 to 15, wherein said pairs of electrodes on said resistive layer comprise strip electrodes disposed along edges of said planar photodiode detector element.

17. A detector according to any of claims 10 to 15, wherein said pairs of electrodes on said resistive layer comprise discrete electrodes disposed at corners of said planar photodiode detector element.

18. A detector according to any of claims 10 to 17, wherein said additional electrode disposed in the central region of said resistive layer has dimensions sufficiently smaller than the smallest beam intended to be measured that the accuracy of the measurement of beam size is not compromised.