CHAPTER 9 POSITION SENSITIVE PHOTOMULTIPLIER TUBES The current multiplication mechanism offered by dynodes makes photomultiplier tubes ideal for low-light-level measurement. As explained earlier, there are various types of dynode structures available for different photometric purposes. Popular conventional dynode structures are the box-and-grid type, linear-focused type, circular-cage type and venetian-blind types. Furthermore, the MCP (microchannel plate) has recently been utilized as a dynode structure. Two unique dynode structures are introduced in this chapter: the "metal channel dynode" and "grid type dynode". These dynode structures provide wide dynamic range, high gain, high position resolution, and are currently used in position-sensitive photomultiplier tubes. Common methods for reading out the output signal from a positionsensitive photomultiplier tube are illustrated in Figure 9-1. In a multianode device, the output signal is read using independent multiple anodes. The cross-plate (wire) anode signal is read out by means of current or charge-dividing center-of-gravity detection. © 2007 HAMAMATSU PHOTONICS K. K. 168 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES MULTI ANODE Y2 RESISTORS CHARGE-DIVISION READOUT CIRCUIT X1 X2 SUM DIV. X= Y1 X2 X1+X2 CROSS-WIRE (PLATE) ANODE THBV3_0901EA Figure 9-1: Anode output readout methods for position sensitive photomultiplier tubes The following sections describe "metal channel dynode structures combined with multianode readout", "metal channel dynode structures combined with a cross-plate anode" and "grid type dynode structures combined with a cross-wire anode" for position sensitive photomultiplier tubes. © 2007 HAMAMATSU PHOTONICS K. K. 9.1 9.1 Multianode Photomultiplier Tubes 169 Multianode Photomultiplier Tubes 9.1.1 Metal channel dynode type multianode photomultiplier tubes (1) Structure Figure 9-2 shows the electrode structure for metal channel dynodes and the associated electron trajectories. Compared to the other types of dynodes, metal channel dynode type multianode photomultiplier tubes feature very low crosstalk during secondary electron multiplication. This is because the photoelectrons emitted from the photocathode are directed onto the first dynode by the focusing mesh and then flow to the second dynode, third dynode, . . . last dynode and finally to the anode, while being multiplied with a minimum spatial spread in the secondary electron flow. The overall tube length can be kept short because the metal channel dynodes are very thin and assembled in close-proximity to each other. PHOTOCATHODE FOCUSING MESH METAL CHANNEL DYNODES MULTIANODE THBV3_0902EA Figure 9-2: Electrode structure and electron trajectories Multianode photomultiplier tubes using metal channel dynodes can be roughly classified into two groups. One group uses a matrix type multianode and the other group uses a linear type multianode. © 2007 HAMAMATSU PHOTONICS K. K. 170 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES Metal Channel Dynode Multianode Photomultiplier Tubes Type Linear Matrix Matrix M4 M16 M64 L16 L32 M64 Number of Anodes 4 16 64 16 32 64 Pixel Size (mm) 9×9 4×4 2×2 0.8 × 16 0.8 × 7 5.8 × 5.8 Anode Shape THBV3_0903EA Figure 9-3: Anode patterns for metal channel dynode type multianode photomultiplier tubes (2) Characteristics In this section, we first describe basic characteristics of matrix type multianode photomultiplier tubes by discussing "crosstalk", "magnetic immunity" and "uniformity" in 64 channel matrix type multianodes. "Crosstalk" is a measure to indicate how accurately the light (signal) incident on a certain position of the photocathode is detected while still retaining the position information. In photomultiplier tube operation, crosstalk is mainly caused by the broadening of the electron flow when light is converted into electrons and those electrons are multiplied by the dynode section. The incident light spread within the faceplate is another probable cause of crosstalk. A typical setup for measuring crosstalk is shown in Figure 9-4 and an example of measurement data in Figure 9-5. UV SPOT LIGHT SOURCE d HIGH VOLTAGE POWER SUPPLY QUARTZ FIBER SCINTILLATING FIBER (KURARAY, L=3 m) PMT AMMETER THBV3_0904EA Figure 9-4: Crosstalk measurement method © 2007 HAMAMATSU PHOTONICS K. K. 9.1 Multianode Photomultiplier Tubes d=0 mm 171 d=0.5 mm 0.3 1.4 0.4 0.4 2.6 0.6 0.8 100 1.2 1.5 100 1.9 0.2 1.1 0.3 0.3 1.8 0.4 SCINTILLATING FIBER (1.0 mm dia.) SUPPLY VOLTAGE: 800 (V) d: DISTANCE SCINTILLATING FIBER (1.0 mm dia.) SUPPLY VOLTAGE: 800 (V) d: DISTANCE THBV3_0905EA Figure 9-5: Crosstalk measurement example Data shown in Figure 9-5 is measured by irradiating a light spot (signal) on the photomultiplier tube faceplate, through a 1 mm diameter optical fiber placed in close contact with the faceplate. The output of each anode is expressed as a relative value, with 100 % being equal to the peak anode output produced from the incident light spot. Results show that crosstalk is 0.2 % to 1.4 % when the 1 mm diameter scintillating fiber is positioned in tight contact with the photomultiplier tube faceplate (d=0 mm). However, the crosstalk becomes 0.3 % to 2.6 % worse when the scintillating fiber is moved 0.5 millimeters away from the faceplate. This is of course due to light spread at the scintillating fiber exit. Bringing the optical fiber into tight contact with the photomultiplier tube faceplate is therefore recommended in order to make accurate measurements using scintillating fibers. Next, let's discuss magnetic characteristics. Matrix type multianode photomultiplier tubes have excellent immunity to magnetic fields. This is because all parts except the photocathode are housed in a metal package and also because the distance between dynode electrodes is very short. Magnetic characteristics of a 64-channel multianode photomultiplier tube are explained below. Figure 9-6 shows how the anode output is adversely affected by external magnetic fields applied along the three axes (X, Y, Z). Each data is plotted as a relative output value, with 100 % corresponding to an output with no magnetic field applied. Output is still maintained as high as 60 % versus 13 mT of the magnetic field in the X direction. 110 + X axis + − X axis 90 RELATIVE OUTPUT (%) Y Z 100 + 80 − 70 Z axis 60 Z axis − 50 Y axis Y axis 40 30 20 10 0 −10 −5 -0 5 Z axis Y axis X axis 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 MAGNETIC FIELD (mT) THBV3_0906EA Figure 9-6: Effects of external magnetic fields on anode output (anode channel No. 29) © 2007 HAMAMATSU PHOTONICS K. K. X 172 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES 100 90 80 70 60 50 40 30 20 10 0 64 1 3 RELATIVE ANODE OUTPUT Figure 9-7 shows typical uniformity data obtained from each anode when uniform light is illuminated over the entire photocathode of a 64-channel multianode photomultiplier tube. The non-uniformity observed here probably originates from gain variations in the secondary electron multiplier because the photocathode itself has good uniformity. Currently, non-uniformity between each anode is about "1:3" on average. 48 5 32 PIXEL NUMBER 7 PIXEL NUMBER 16 THBV3_0907EA Figure 9-7: 64-channel multianode output uniformity Uniformity of one pixel (one anode) is shown in Figure 9-8. This data is measured by input of weak DC light of 50 µm diameter to an anode of 2 square millimeters per pixel, while scanning the light every 0.1 millimeters on the photocathode. 0 0.5 1 RELATIVE OUTPUT 100 90 80 70 60 50 40 30 20 10 0 4 3.5 3 1.5 2.5 2 2 mm 1.5 2.5 1 3 mm 0.5 3.5 4 0 THBV3_0908EA Figure 9-8: Anode output uniformity per pixel © 2007 HAMAMATSU PHOTONICS K. K. 9.1 Multianode Photomultiplier Tubes 173 We next describe basic "crosstalk" and "uniformity" characteristics of linear multianode photomultiplier tubes. A typical setup for measuring crosstalk of a 16-channel linear multianode photomultiplier tube is shown in Figure 9-9 and the typical measurement data in Figure 9-10. In this measurement, a light spot emitted through the 100 µm aperture in the X-Y stage was scanned along the photocathode. Typical crosstalk obtained from the 16-channel linear multianode was approximately 3 %. DARK BOX X-Y STAGE CONTROLLER CHANNEL CHANGER X-Y STAGE GP-IB LAMP BOX LAMP POWER SUPPLY HIGH VOLTAGE POWER SUPPLY AMMETER PC THBV3_0909EA Figure 9-9: Crosstalk measurement method OUTPUT DEVIATION (%) SPATIAL RESOLUTION AND CROSSTALK SCAN SCAN POSITION 100 80 DEAD SPACE EFFECTIVE SPACE 60 1 CH SIGNAL B A 20 0 16 CH (TOP VIEW) 40 1 2 3 4 5 6 7 SUPPLY VOL.: -800 V LIGHT SOURCE: TUNGSTEN LAMP SPOT DIA.: 100 µm SCAN PITCH: 50 µm POSITION (channelsd) CH 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 CROSS-TALK RATIO (%) 1 2 3 4 5 6 7 8 9 10 11 100 2.9 0.6 0.2 0.1 — — — — — — 2.9 100 3.1 0.5 0.2 0.1 — — — — — 0.8 2.8 100 2.8 0.6 0.2 0.1 — — — — 0.3 0.8 2.7 100 3.2 0.6 0.2 0.1 — — — 0.1 0.3 0.8 2.9 100 3.1 0.6 0.2 0.1 — — — 0.1 0.3 0.8 2.7 100 3.0 0.6 0.2 0.1 — — — 0.1 0.3 0.8 2.7 100 3.0 0.6 0.2 0.1 — — — 0.1 0.3 0.8 2.9 100 2.9 0.6 0.2 — — — — 0.1 0.3 0.8 2.9 100 2.9 0.6 — — — — — 0.1 0.3 0.8 3.1 100 2.7 — — — — — — 0.1 0.4 0.8 3.3 100 — — CROSSTALK — — — — — 0.1 0.4 0.9 3.2 — AREA — B—/ AREA — A—× 100 — — — 0.1 0.4 0.8 — — — — — — — — — 0.1 0.4 — — — — — — — — — — 0.1 — — — — — — — — — — — 12 — — — — — — — 0.1 0.2 0.6 3.8 100 3.1 0.8 0.4 0.1 13 — — — — — — — — 0.1 0.2 0.6 2.8 100 3.1 0.9 0.4 14 — — — — — — — — — 0.1 0.2 0.6 2.8 100 3.2 0.9 15 — — — — — — — — — — 0.1 0.2 0.6 2.7 100 3.1 16 — — — — — — — — — — — 0.1 0.3 0.6 2.9 100 THBV3_0910EA Figure 9-10: Crosstalk of 16-channel linear anode © 2007 HAMAMATSU PHOTONICS K. K. 174 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES Some 16-channel and 32-channel linear multianode photomultiplier tubes are low crosstalk types. Some use a special faceplate containing black glass partitions or an electrode structure having shielding walls between the anodes of each channel. Typical crosstalk values measured with a low crosstalk type are shown in Figure 9-11. 5.0 LOW CROSSTALK TYPE 4.0 CONVENTIONAL TYPE 3.0 2.0 5 ch 6 ch 7 ch 8 ch 9 ch ch ch 16 ch 4 15 ch ch 3 13 ch 14 ch ch ch 2 12 ch 11 1 10 0.0 ch 1.0 THBV3_0911EA Figure 9-11: Crosstalk values of 16-channel low-crosstalk type Figure 9-12 shows typical uniformity data of a linear multianode photomultiplier tube. This data was obtained from each anode when uniform light was illuminated over the entire photocathode of a 32-channel linear multianode photomultiplier tube. As with the matrix type, non-uniformity mainly originates from gain variations in the secondary electron multiplier. Currently, non-uniformity between each anode is about "1:1.7" on average. OUTPUT DEVIATION (%) 100 80 60 40 20 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 CHANNEL THBV3_0912EA Figure 9-12: 32-channel linear multianode output uniformity © 2007 HAMAMATSU PHOTONICS K. K. 9.1 Multianode Photomultiplier Tubes 175 Since 16-channel and 32-channel linear multianode photomultiplier tubes have a one-dimensional array of anodes, they are mainly used as detectors for multichannel spectrophotometry. Due to its shape, the 32channel type is often used in combination with a grating or prism, and recent applications include laser scanning microscopes. Linear multianode photomultiplier tubes are also available with a band-pass filter attached to the faceplate. This allows detecting light only in the wavelength range of interest, just like using a grating or prism. There is no loss of light caused by the entrance slit which is used with the grating for separating the light into different wavelengths. Since light must uniformly strike the entire surface of the band-pass filter, Hamamatsu also provides a dedicated mixing fiber combined with a lens for this purpose. Figure 9-13 shows a photomultiplier tube with a band-pass filter and a dedicated mixing fiber combined with a lens. Figure 9-13: Photomultiplier tube with band-pass filter Mixing fiber + lens Dichroic mirrors can also be used for dispersing light into a spectrum. One example is illustrated in Figure 9-14 showing a very compact device containing an optical system and a detector. DICHROIC MIRROR MIRROR LIGHT BPF BPF BPF BPF PHOTOCATHODE LINEAR MULTIANODE PMT A ch B ch C ch D ch ANODE THBV3_0914EA Figure 9-14: Multianode photomultiplier tube assembled with dichroic mirrors © 2007 HAMAMATSU PHOTONICS K. K. 176 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES 9.1.2 Multianode MCP-PMT The multianode MCP-PMT is explained in detail in section 10.4 of Chapter 10. 9.1.3 Flat panel type multianode photomultiplier tubes (1) Characteristics Metal channel dynodes are mainly used in 1-inch square metal package photomultiplier tubes and flat panel type (2 square inches) photomultiplier tubes, which can be selected according to the particular application. This section introduces a flat panel type photomultiplier tube with an overall height as short as 15 millimeters. As shown in Figure 9-15, this photomultiplier tube features a large effective area and minimal dead area (insensitive area). 3/4-inch circular type 1-inch square type (with no flange) 25.7 mm 25.7 mm Effective Area 22 mm Effective Area 24 mm 73 % 87 % Flat panel type 52.0 mm 32.2 mm 32.2 mm 1-inch square type (with flange) Effective Area 15 mm 59 % 49 mm 89 % THBV3_0915EA Figure 9-15: Comparison of effective area ratio Typical spatial resolution obtained with a flat panel type 64-channel photomultiplier tube is shown in Figure 9-16. This spatial resolution data (output distribution of each anode) was measured by scanning the photocathode surface with a 1-millimeter collimated light beam emitted from a tungsten lamp through a blue filter. © 2007 HAMAMATSU PHOTONICS K. K. 9.1 Multianode Photomultiplier Tubes 177 Y-axis Supply Voltage: 1000 V Spot Diameter: 1.0 mm Scanning Pitch: 0.1 mm X-axis Cross Uniformity of X-Axis Cross Uniformity of Y-Axis 100 Relative Anode output (%) Relative Anode output (%) 100 80 60 40 20 0 0 5 10 15 20 25 30 35 80 60 40 20 0 40 0 5 10 Position (mm) 15 20 25 30 35 40 Position (mm) THBV3_0916EA Figure 9-16: Spatial resolution of center anodes Figure 9-17 shows typical crosstalk characteristics measured by irradiating the center of an anode (anode pitch 6 mm) with a light beam of 5 square millimeters. Relative outputs of adjacent anodes are shown in the figure by setting the output of this anode as 100 %,. As can be seen in the figure, this flat panel type 64-channel multianode photomultiplier tube has a crosstalk of 2 to 3 % at the center anodes. — — — — — — 0.2 1.8 0.2 — — 1.5 100 2.7 — — 0.2 2.6 0.3 — — — — — — Supply Voltage: 1000 V Light Source: Tungsten Lamp Spot Size: 5 square millimeters THBV3_0917EA Figure 9-17: Crosstalk characteristics of center anodes © 2007 HAMAMATSU PHOTONICS K. K. 178 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES To take full advantage of the effective area, the photoelectrons emitted from the edges of the photocathode are focused toward the dynodes. This tends to increase anode crosstalk (3 % to 6 %) particularly in the corner areas. (See Figure 9-18.) 100 5.5 — 3.5 0.5 — — — — Supply Voltage: 1000 V Light Source: Tungsten Lamp Spot Size: 5 square millimeters THBV3_0918EA Figure 9-18: Crosstalk characteristics of anodes in corner area 9.2 Center-of-Gravity Position Sensitive Photomultiplier Tubes 9.2.1 Metal channel dynode type multianode photomultiplier tubes (cross-plate anodes) (1) Structure Figure 9-19 shows the electrode structure of a metal channel dynode type multianode photomultiplier tube using a cross-plate anode. In this photomultiplier tube, photoelectrons emitted from the photocathode are multiplied by each dynode and the multiplied secondary electrons are then reflected back from the last dynode and read out from the plate type anodes (cross-plate anodes) arranged in two layers intersecting with each other. PHOTOCATHODE FOCUSING MESH METAL CHANNEL DYNODES X ANODE Y ANODE LAST DYNODE CROSS-PLATE ANODE TYPE THBV3_0919EA Figure 9-19: Electrode structure © 2007 HAMAMATSU PHOTONICS K. K. 9.2 Center-of-Gravity Position Sensitive Photomultiplier Tubes 179 Figure 9-20 illustrates the center-of-gravity detection method for reading out the output signal from a position-sensitive photomultiplier tube using a cross-plate anode. The electron bunch released from the last dynode is collected by anodes linearly arranged in the X and Y directions. Since each anode in the same direction is connected by a resistor string, the collected electrons are divided into four signal components X1, X2, Y1 and Y2 corresponding to the anode position at which the secondary electrons arrive. By inputting these signals to summing (SUM) and divider (DIV) circuits, the center of gravity in the X and Y directions can be obtained from Eq. 9-1. X= X2 (X1+X2) Y= Y2 ................................................................................ (Eq. 9-1) (Y1+Y2) Y2 RESISTORS RESISTORS Y1 X1 SUM X2 DIV X= X2 X1+X2 THBV3_0920EA Figure 9-20: Center-of-gravity measurement method (2) Characteristics This section describes spatial resolution characteristics obtained by center-of-gravity detection using 6(X) + 6(Y) cross-plate anodes respectively arranged in the XY directions. This spatial resolution data (output distribution of each anode) was measured by scanning the photocathode surface with a 1-millimeter collimated light beam emitted from a tungsten lamp. Results are shown in Figures 9-21 and 9-22. © 2007 HAMAMATSU PHOTONICS K. K. CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES 100 RELATIVE OUTPUT (%) 80 PX1 PX2 PX3 PX4 PX5 PX6 60 40 20 0 0 10 20 30 POSITION (mm) SUPPLY VOLTAGE : -800 V : TUNGSTEN LAMP LIGHT SOURCE SPOT DIAMETER : 1 mm THBV3_0921EA Figure 9-21: Spatial resolution of X anodes 100 80 RELATIVE OUTPUT (%) 180 PY1 PY2 PY3 PY4 PY5 PY6 60 40 20 0 0 10 20 30 POSITION (mm) SUPPLY VOLTAGE : -800 V : TUNGSTEN LAMP LIGHT SOURCE SPOT DIAMETER : 1 mm THBV3_0922EA Figure 9-22: Spatial resolution of Y anodes © 2007 HAMAMATSU PHOTONICS K. K. 9.2 Center-of-Gravity Position Sensitive Photomultiplier Tubes 181 Figure 9-23 introduces a circuit diagram for scintillation imaging of 511 keV gamma-rays. It utilizes a position sensitive photomultiplier tube with 6(X) + 6(Y) cross-plate anodes and a mosaic array of scintillators (BGO of 2.2 mm×2.2 mm×15 mm arranged in a pattern of 9×9=81 pieces). An actual image obtained is shown in Figure 9-24. PX1 X1 INTEGRATION A/D PX2 PX3 X1 X1 + X2 PX4 9 × 9 BGO ARRAY X ADDRESS PX5 PX6 X2 PY1 Y1 INTEGRATION A/D INTEGRATION A/D PY2 Y ADDRESS PY3 Y1 Y1 + Y2 PY4 PY5 PY6 Y2 INTEGRATION Sum A/D EVENT DETECTION ENERGY DISCRI. EVENT SIGNAL THBV3_0923EA Figure 9-23: Scintillation imaging circuit using gamma-rays irradiated on mosaic pattern scintillators (BGO) Figure 9-24: Scintillation image obtained by gamma-rays irradiated on mosaic pattern scintillators (BGO) This scintillation imaging shows the mosaic pattern of 81 (9×9) BGO scintillators (2.2 mm×2.2 mm×15 mm). Off-center distortion in the image can be corrected by a lookup table. © 2007 HAMAMATSU PHOTONICS K. K. 182 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES 9.2.2 Grid type dynode photomultiplier tubes (Cross-wire anodes) (1) Structure Figure 9-25 shows the electrode structure for grid type dynodes and the associated electron trajectories. The significant difference compared to ordinary box-and-grid dynodes is that the electron multiplier is fabricated from flat grid-like dynodes. These dynodes have a very fine structure that emits secondary electrons while suppressing the spatial spread of secondary electrons at each dynode. In this photomultiplier tube, photoelectrons emitted from the photocathode are multiplied by each dynode (up to a total gain of 105 or more) and then the multiplied secondary electrons are reflected back from the last dynode (reflection type) and read out from the wire type anodes (cross-wire anodes) arranged in two layers intersecting with each other. The first dynode is placed in close proximity to the photocathode to minimize the spatial spread of photoelectrons. PHOTON PHOTOCATHODE FOCUSING MESH GRID TYPE DYNODES X ANODE Y ANODE Y LAST DYNODE 0 X THBV3_0925EA Figure 9-25: Electrode structure and electron trajectories (2) Characteristics A photomultiplier tube using a 12-stage grid type dynode yields a gain of 105 or more at 1250 volts. This type of photomultiplier tube is available in a circular envelope of 3 or 5 inches in diameter. The number of wire anodes in the X and Y directions is 16(X) + 16(Y) for the 3-inch circular type (anode pitch: 3.75 millimeters) and 28(X) + 28(Y) for the 5-inch circular type (anode pitch: 4 millimeters). Next, let's discuss the center-of-gravity detection method and spatial resolution characteristics. As shown in Figure 9-25, the electron flow spreads spatially between the photocathode and the first dynode and also between each grid dynode. When 50 µm diameter light spot scans the photocathode surface of the 3-inch circular type photomultiplier tube, the X and Y direction spatial resolutions are obtained as shown in Figures 9-27 and 9-28. Since the electron flow spreads in the multiplication process from the photocathode to the anode, the width of spatial resolution measured at each anode broadens to 9.5 millimeters in the X direction and to 8.6 millimeters in the Y direction. Figure 9-26: Grid type dynode photomultiplier tube © 2007 HAMAMATSU PHOTONICS K. K. 9.2 Center-of-Gravity Position Sensitive Photomultiplier Tubes 183 FWHM=9.5 (mm) 100 X9 RELATIVE OUTPUT (%) 80 X10 60 40 20 0 0 15 30 45 60 75 POSITION (mm) THBV3_0927EA Figure 9-27: Spatial resolution in X direction FWHM=8.6 (mm) 100 Y8 RELATIVE OUTPUT (%) 80 Y9 60 40 20 0 0 15 30 45 60 75 POSITION (mm) THBV3_0928EA Figure 9-28: Spatial resolution in Y direction © 2007 HAMAMATSU PHOTONICS K. K. 184 CHAPTER 9 POSITION-SENSITIVE PHOTOMULTIPLIER TUBES To read out the signal from this photomultiplier tube, the center-of-gravity detection method is used, as described in the previous section 9.2.1, "Metal channel dynode type multianode photomultiplier tubes (cross-plate anodes)". Figure 9-29 shows plots of spatial resolution measured with light emitted from a pulsed LED while changing the amount of light per pulse. This spatial resolution is determined by the center-of-gravity distribution in the output signal that broadens almost in inverse proportion to the square root of the amount of incident light according to the statistical theory. Figure 9-30 shows the center-of-gravity distribution characteristics measured while moving a light spot on the photocathode in 1 millimeter intervals. It proves that a resolution of 0.3 millimeters (FWHM) is obtained in the center at a light intensity of 4000 photons per pulse. A slight distortion occurs near the off-center region because there are fewer cross-wire anodes involved in the output signal. Figure 9-31 is a spatial linearity graph showing the electrical center-ofgravity position on the vertical axis and the light spot position on the horizontal axis. at 560nm SPATIAL RESOLUTION (FWHM) (mm) 1.0 0.8 0.5 0.4 0.2 0.1 100 1000 10000 100000 NUMBER OF INCIDENT PHOTONS (Photons per event) THBV3_0929EA Figure 9-29: Spatial resolution vs. incident light level COUNT PER CHANNEL ANODE PITCH : 4 mm LIGHT LEVEL : 4000 photons/event 0.3 mm FWHM 1 mm CHANNEL NUMBER THBV3_0930EA Figure 9-30: Center-of-gravity distribution with light spot movement © 2007 HAMAMATSU PHOTONICS K. K. 9.2 Center-of-Gravity Position Sensitive Photomultiplier Tubes 185 RELATIVE POSITION SIGNAL 100 80 60 40 20 0 10 20 30 40 50 60 70 80 90 100 110 120 X AXIS (mm) THBV3_0931EA Figure 9-31: Spatial linearity of grid type dynode photomultiplier tube In the peripheral portion of the photomultiplier tube, not all electrons are focused by the cross-wire anodes, and these electrodes cause distortion as if they are drawn toward the center. But this distortion level is small enough to be corrected by a lookup table or similar techniques. © 2007 HAMAMATSU PHOTONICS K. K. MEMO © 2007 HAMAMATSU PHOTONICS K. K.