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Modulation Transfer Function Measurements on Channel Image Intensifies
Modulation Transfer Function Measurements on Channel Image Intensifiers E. C . YEADON Mulhrd Mitcham, New Road,Mitcham, Surrey, England and
J. A. CLARKE Mullard Reaearch Laboratories, Redhill, Surrey, England
INTRODUCTION In recent years, the modulation transfer function (m.t.f.) has been increasingly regarded as one of the most important ways of describing image quality. In this paper the application of the m.t.f. to a particular type of imaging device will be considered and some pitfalls which must be avoided if meaningful measurements are to be obtained will be pointed out. The channel image intensifier tube which is the subject of these measurements is described in detail by Emberson and Holmshaw elsewhere in these proceedings,? and will not be further described here. If transfer functions are to be applicable to an image transfer process, the necessary conditions €or Fourier transformation must be satisfied. That is, the process must be linear in response and spatially stationary. Channel-plate image intensifiers satisfy neither of these conditions in general.
REQUIREMENTS FOR M.T.F. MEASUREMENT Linearity The first requirement is linearity. If this is not satisfied, the intensity
distribution in the image will be distorted resulting in the generation of higher harmonics, so that linear analysis is invalid. The response of channel electron multipliers is only linear up to a certain current level, after which saturation effects begin to show, a typical characteristic being shown in Fig. 1. The output screen luminance Loa t which
t See paper 19 p.
133. 593
<594
E. C. YEADOK AND J. A. CLARKE
there is a discontinuity depends on several tube parameters, such as screen efficiency, channel-plate gain, etc., and may be as low as 10 cd/m2. It is essential that if an m.t.f. is being measured, no point in the screen image should exceed this limiting luminance.
Log cathode illumination ( E , )
FIG.1. Typical transfer characteristic response of a channel image intensifier.
The effect on the measured m.t.f. if the linearity limit is exceeded is illustrated in Fig. 2. Measured m.t.f.’s are shown for gradually increasing levels of cathode illumination Ei. Figure 3 shows the same data re-plotted to illustrate the uniform m.t.f. in the linear region and t,he fall in the m.t.f. as soon as the discontinuity is reached.
Spatial frequency of screen (cycledrnm)
FIG.2. Muasurcd m.t.f.
of a channel image intensifier as the cathode illuminatioll E’, is increased through t,he discontinuous region.
MTF MEASUREMENTS ON CHANNEL IMAGE INTENSIFIERS 10
1
1
I
I
595
I
I 5 cycles/mm
Loq cathode illumtnafian E, i lm/m2)
FIG.5. Variation of measured tn.t.f. with rathoclo illumination.
Ntntionarify The channel plate consists of a large number of electron multiplier tubes in a hexagonal array. Figure 4 shows how the image of a sharp slit through such an array of apertures depends on the relative position of the slit on the array. This is a violation of the condition of stationarity and there will not be a unique m.t.f. which will relate the output image to the input image. If the slit is very long and not aligned with a principal axis of the array, the output image, averaged over the length of the slit, becomes independent of the position of the slit on the array. If, in addition, the pattern which is imaged through the device is limited to low spatial frequencies, the practical limit of which can be calculated from the spacing of the array elements by means of the Sampling Theorem,l the imaging process can be regarded as being stationary over t h e restricted spatial frequency range involved. The reasons for this are obvious if one considers the signal (image) being used to modulate a carrier frequency (the sampling array of the plate). Instead of being a harmonically pure sine wave, the carrier frequency is, in fact, a form of square wave with a series of harmonics distributed a t equal intervals throughout the spatial frequency spectrum. If the spatial bandwidth of the image is too great, neighbouring spectral orders will overlap giving the effect known as frequency
596
E. 0 . YEADON AND J. A. CLARKE
folding, aliassing or, when extended to two dimensions, moire fringes. If the spatial bandwidth is restricted so that there is no overlap, signal spatial frequencies in the zero order (i.e. distributed about zero spatial frequency) can be considered to be unaffected by the sampling process so that stationarity is preserved.
..e ..
- 1
Fro. 4. Slit sarnplctl by chaiinol plate array.
APPARATUS Because of the finite decay time of the screen phosphor, measurement of the m.t.f. must be made with a test pattern which does not move with time. I n many instruments the test pattern is a narrow slit which is imaged on to the photocathode. The resulting line-spread function on the output screen is analysed to obtain the m.t.f. Because of the constraint on screen brightness for linearity, a long slit will give a better signal-to-noise ratio than a short slit. At the same time, the slit must not be so long that the m.t.f. changes significantly along the length, or that, for off-axis measurements, distortion in the electron optics causes the image to be curved. We have used a number of methods to measure the m.t.f. of channel tubes. A simple method we have used extensively is to measure the profile of the line-spread function with a scanning microphotometer. This is a relatively cheap and extremely versatile piece of equipment consisting of a microscope objective, slit, and photomultiplier, all mounted on a cross-slide driven by a synchronous motor as shown in Pig. 5 . The output, after amplification, can be taken to a pen-recorder or a digital voltmeter and paper tape punch. The recorded data are subsequently used to compute the m.t.f. by Fourier transformation.
MTF MEASUREMENTS ON CIIANKEL IMAGE INTENSIFIERS
597
The digital voltmeter has a range greater than 4 decades and the pen-recorder can be read over a range of 2 decades. Care must be taken to scan sufficiently far on either side of the central peak, otherwise the results a t low spatial frequencies will be too high. We have also tried two commercially available m.t.f. measuring equipments. The requirement regarding length of slit rules out apparatus such as the SIRA-Beck EROS 110 in which only a very short length of the line-spread function is passed to the analyser, resulting in an extremely noisy signal. The Oude Delft ODETA-2
-3, voltmeter
Paper
I
OFF -' L I NE t o computer for m t f analysis
FIG.5. Microphotometer for sprrad-function measurements.
equipment does not suffer from the length of slit being inadequate, but it was found that the amplifier was not sensitive enough for our purposes and was also non-linear a t very low signal levels. A modified amplifier, provided by Oude Delft, has recently been tried. This has 10 times more gain and the linear range at the lower end extends to a t least another decade, resulting in 100 times more useful range. With the scanning microphotometer, there is a delay for computation before the m.t.f. results are known, but the ODETA trace is available for immediate visual assessment. This makes adjustments to the system, such as focusing the slit, very much easier. The ODETA is the most convenient of all the methods we have tried. Some method of controlling the illumination on the photocathode is essential, whatever the method of measuring the m.t.f. since serious errors can result from visual judgment of the onset of saturation in the tube. With the addition of a calibrated optical attenuator a t
598
E. C. YEADON A N D J. A. CLARKE
the light source, the ODETA can actually be used to measure the transfer characteristic curve of the tube, so that operation within the linear region can be ensured.
Low Frequency Contrast and Zero Normalization Light emitted by the phosphor screen may be reflected from the channel plate to illuminate the screen a short distance away. This will add to any general background on the tube and appear in the m.t.f. as a rapid drop a t low spatial frequencies. This has been eliminated from most of our measurements by extrapolating back from the continuous curve as shown in Fig. 6 and using this value for normalization.
PIG. 6. Modulation transfer function trace showing method of zero-frequency extrapolation arid normalization.
The ratio OA/OB represents the “low frequency contrast” and is found to agree well with the 80% or so determined from separate large-area square-wave modulation measurements. The ratio OA/OB, however, will also depend on the area of screen a t which the analyser is looking (i.e. on the diameter of the analyser window and the magnification of the relay lens) and is, in practice, useful only for relative measurements.
Noise Channel image intensifiers are inherently more noisy than conventional types. This noise appears as fluctuations on the m.t.f. trace and is made worse in many cases by the necessity to work a t very low screen brightness levels, to ensure linearity. Figure 7 shows an actual m.t.f. trace from the ODETA on a tube with screen luminance about 2 cd/m2. At high spatial frequencies the modulus is near
MTF MEASUREMENTS ON CHANNEL IMAGE INTENSIFIERS
599
zero, but because the system also adds the frequency components present in the noise, the apparent m.t.f. will be higher than the true m.t.f. The error is obvious in Fig. 7 where a noise-free 1n.t.f. from the same tube has been plotted by running a t it higher screen luminance level, but still well below the discontinuity in the tube characteristic. The magnitude of the systematic error depends on the signal-to-noise ratio and on the statistics of the noise fluctuations. True correction for the effect is exceedingly difficult and calls for rather sophisticated signal averaging, but a certain ainourit of allowance can be made subjectively by hand-smoothing a noisy trace. I
I
Spatial frequency
FIG.7. Cornparison of high-noise and lorn-noise tracrs showing systematic r m w dueto noim at high spatial fieqncmcirs.
The same type of error can result from noisy spread-function data. Hand smoothing the noisy spread-function traces will not necessarily reduce random errors in the m.t.f. without the possibility of incurring systematic errors.
REMARKS ON THE USE OF M.T.F. TO CHARACTERIZE A NON-LINEAR, NON-STATIONARY DEVICE The above restrictions on the conditions for measuring a m.t,.f. may not be satisfied in the practical application of the channel tlube. If the screen is to be examined visually, the image may be no less useful for all that it is non-linear and non-stationary. Indeed, sornetimes a non-linear response is an advantage for very high scene contrasts and is often encouraged to obtain tone compression in the highlights. I n such circumstances a tube characteristic n1.t.f. which is
600
E. C. YEADON AND J . A . CLARKE
measured in such a way in order to avoid the mathematical complexities of non-linearity and non-stationarity may not be relevant to the tube in the conditions of use. As long as a unique tube m.t.f. is required, it is essential to take all the precautions necessary to ensure validity of the result. But consideration should also be given to the intended use and, where a non-linear response is expected, it is important to use the normal subjective criteria of image-quality assessment to supplement the results of linear analysis.
REFERENCE 1. Papoulis, A., “Systems and Transforms with Applications in Optics,” McGrawHill, New York, (196s).
DISCUSSION w. L. WILCOCK: Would it not be possible to extend the frequency region in which the m.t.f. can be usefully defined by introducing lateral motion of the image tube relative to the observer, for example, by small amplitude vibrations? E. 0.YEADON : Dynamic scanning would indeed get round some of the difficulties of the sampled image. But) any movement of the image over the tube would effectively reduce the m.t.f. because of the persistence time of the phosphor screen. The form of dynamic scanning that would most improve the image would be lateral motion of the channel plate, with the image stationary on the screen. This would be impractical in such a short tube. H. BONQARTZ: Did your image intensifier have a fibre-optic plate on the photocathode side 7 It is possible that the auto-correlation functions (or radial distribution functions) of the fibre-optic plate and the channel plate have the same form but different correlation lengths. It is also possible that there is a non-zero correlation between the two plates, in which case you may not combine the m.t.f.’s. Did you find any evidence of this? E. 0.YEADON : The fibre-optic plate at the photocathode has fibres arranged on a square lattice of 7 pm pitch. This is too high a spatial frequency to be sharply imaged on the channel plate by the electron optical imaging stage, and the image formed on the channel plate is effectively continuous. We have seen no evidence at all of intorference between the square fibre-optic lattice and the hexagonal packing lattice of the channel plate. E. w. DENNISON: With reference to the imaging between the channel plate and the output screen, what difference would you oxpect betweon proximity focusing and magnetic focusing? E. c . YEADON : Magnetic focusing would be expected to improve the sharpness of the image on the screen. But proximity focusing is already good enough to resolve the individual channel spots, and any further improvement could only be marginal from the point of view of information transfer. Magnetic focusing would increase the size and weight of the tube, and there would be difficulties in isolating the electrostatic focused inverter section from the very high magnetic field which would be necessary to form the image in the space available.
J. A. CLARKE Mullard Reaearch Laboratories, Redhill, Surrey, England
INTRODUCTION In recent years, the modulation transfer function (m.t.f.) has been increasingly regarded as one of the most important ways of describing image quality. In this paper the application of the m.t.f. to a particular type of imaging device will be considered and some pitfalls which must be avoided if meaningful measurements are to be obtained will be pointed out. The channel image intensifier tube which is the subject of these measurements is described in detail by Emberson and Holmshaw elsewhere in these proceedings,? and will not be further described here. If transfer functions are to be applicable to an image transfer process, the necessary conditions €or Fourier transformation must be satisfied. That is, the process must be linear in response and spatially stationary. Channel-plate image intensifiers satisfy neither of these conditions in general.
REQUIREMENTS FOR M.T.F. MEASUREMENT Linearity The first requirement is linearity. If this is not satisfied, the intensity
distribution in the image will be distorted resulting in the generation of higher harmonics, so that linear analysis is invalid. The response of channel electron multipliers is only linear up to a certain current level, after which saturation effects begin to show, a typical characteristic being shown in Fig. 1. The output screen luminance Loa t which
t See paper 19 p.
133. 593
<594
E. C. YEADOK AND J. A. CLARKE
there is a discontinuity depends on several tube parameters, such as screen efficiency, channel-plate gain, etc., and may be as low as 10 cd/m2. It is essential that if an m.t.f. is being measured, no point in the screen image should exceed this limiting luminance.
Log cathode illumination ( E , )
FIG.1. Typical transfer characteristic response of a channel image intensifier.
The effect on the measured m.t.f. if the linearity limit is exceeded is illustrated in Fig. 2. Measured m.t.f.’s are shown for gradually increasing levels of cathode illumination Ei. Figure 3 shows the same data re-plotted to illustrate the uniform m.t.f. in the linear region and t,he fall in the m.t.f. as soon as the discontinuity is reached.
Spatial frequency of screen (cycledrnm)
FIG.2. Muasurcd m.t.f.
of a channel image intensifier as the cathode illuminatioll E’, is increased through t,he discontinuous region.
MTF MEASUREMENTS ON CHANNEL IMAGE INTENSIFIERS 10
1
1
I
I
595
I
I 5 cycles/mm
Loq cathode illumtnafian E, i lm/m2)
FIG.5. Variation of measured tn.t.f. with rathoclo illumination.
Ntntionarify The channel plate consists of a large number of electron multiplier tubes in a hexagonal array. Figure 4 shows how the image of a sharp slit through such an array of apertures depends on the relative position of the slit on the array. This is a violation of the condition of stationarity and there will not be a unique m.t.f. which will relate the output image to the input image. If the slit is very long and not aligned with a principal axis of the array, the output image, averaged over the length of the slit, becomes independent of the position of the slit on the array. If, in addition, the pattern which is imaged through the device is limited to low spatial frequencies, the practical limit of which can be calculated from the spacing of the array elements by means of the Sampling Theorem,l the imaging process can be regarded as being stationary over t h e restricted spatial frequency range involved. The reasons for this are obvious if one considers the signal (image) being used to modulate a carrier frequency (the sampling array of the plate). Instead of being a harmonically pure sine wave, the carrier frequency is, in fact, a form of square wave with a series of harmonics distributed a t equal intervals throughout the spatial frequency spectrum. If the spatial bandwidth of the image is too great, neighbouring spectral orders will overlap giving the effect known as frequency
596
E. 0 . YEADON AND J. A. CLARKE
folding, aliassing or, when extended to two dimensions, moire fringes. If the spatial bandwidth is restricted so that there is no overlap, signal spatial frequencies in the zero order (i.e. distributed about zero spatial frequency) can be considered to be unaffected by the sampling process so that stationarity is preserved.
..e ..
- 1
Fro. 4. Slit sarnplctl by chaiinol plate array.
APPARATUS Because of the finite decay time of the screen phosphor, measurement of the m.t.f. must be made with a test pattern which does not move with time. I n many instruments the test pattern is a narrow slit which is imaged on to the photocathode. The resulting line-spread function on the output screen is analysed to obtain the m.t.f. Because of the constraint on screen brightness for linearity, a long slit will give a better signal-to-noise ratio than a short slit. At the same time, the slit must not be so long that the m.t.f. changes significantly along the length, or that, for off-axis measurements, distortion in the electron optics causes the image to be curved. We have used a number of methods to measure the m.t.f. of channel tubes. A simple method we have used extensively is to measure the profile of the line-spread function with a scanning microphotometer. This is a relatively cheap and extremely versatile piece of equipment consisting of a microscope objective, slit, and photomultiplier, all mounted on a cross-slide driven by a synchronous motor as shown in Pig. 5 . The output, after amplification, can be taken to a pen-recorder or a digital voltmeter and paper tape punch. The recorded data are subsequently used to compute the m.t.f. by Fourier transformation.
MTF MEASUREMENTS ON CIIANKEL IMAGE INTENSIFIERS
597
The digital voltmeter has a range greater than 4 decades and the pen-recorder can be read over a range of 2 decades. Care must be taken to scan sufficiently far on either side of the central peak, otherwise the results a t low spatial frequencies will be too high. We have also tried two commercially available m.t.f. measuring equipments. The requirement regarding length of slit rules out apparatus such as the SIRA-Beck EROS 110 in which only a very short length of the line-spread function is passed to the analyser, resulting in an extremely noisy signal. The Oude Delft ODETA-2
-3, voltmeter
Paper
I
OFF -' L I NE t o computer for m t f analysis
FIG.5. Microphotometer for sprrad-function measurements.
equipment does not suffer from the length of slit being inadequate, but it was found that the amplifier was not sensitive enough for our purposes and was also non-linear a t very low signal levels. A modified amplifier, provided by Oude Delft, has recently been tried. This has 10 times more gain and the linear range at the lower end extends to a t least another decade, resulting in 100 times more useful range. With the scanning microphotometer, there is a delay for computation before the m.t.f. results are known, but the ODETA trace is available for immediate visual assessment. This makes adjustments to the system, such as focusing the slit, very much easier. The ODETA is the most convenient of all the methods we have tried. Some method of controlling the illumination on the photocathode is essential, whatever the method of measuring the m.t.f. since serious errors can result from visual judgment of the onset of saturation in the tube. With the addition of a calibrated optical attenuator a t
598
E. C. YEADON A N D J. A. CLARKE
the light source, the ODETA can actually be used to measure the transfer characteristic curve of the tube, so that operation within the linear region can be ensured.
Low Frequency Contrast and Zero Normalization Light emitted by the phosphor screen may be reflected from the channel plate to illuminate the screen a short distance away. This will add to any general background on the tube and appear in the m.t.f. as a rapid drop a t low spatial frequencies. This has been eliminated from most of our measurements by extrapolating back from the continuous curve as shown in Fig. 6 and using this value for normalization.
PIG. 6. Modulation transfer function trace showing method of zero-frequency extrapolation arid normalization.
The ratio OA/OB represents the “low frequency contrast” and is found to agree well with the 80% or so determined from separate large-area square-wave modulation measurements. The ratio OA/OB, however, will also depend on the area of screen a t which the analyser is looking (i.e. on the diameter of the analyser window and the magnification of the relay lens) and is, in practice, useful only for relative measurements.
Noise Channel image intensifiers are inherently more noisy than conventional types. This noise appears as fluctuations on the m.t.f. trace and is made worse in many cases by the necessity to work a t very low screen brightness levels, to ensure linearity. Figure 7 shows an actual m.t.f. trace from the ODETA on a tube with screen luminance about 2 cd/m2. At high spatial frequencies the modulus is near
MTF MEASUREMENTS ON CHANNEL IMAGE INTENSIFIERS
599
zero, but because the system also adds the frequency components present in the noise, the apparent m.t.f. will be higher than the true m.t.f. The error is obvious in Fig. 7 where a noise-free 1n.t.f. from the same tube has been plotted by running a t it higher screen luminance level, but still well below the discontinuity in the tube characteristic. The magnitude of the systematic error depends on the signal-to-noise ratio and on the statistics of the noise fluctuations. True correction for the effect is exceedingly difficult and calls for rather sophisticated signal averaging, but a certain ainourit of allowance can be made subjectively by hand-smoothing a noisy trace. I
I
Spatial frequency
FIG.7. Cornparison of high-noise and lorn-noise tracrs showing systematic r m w dueto noim at high spatial fieqncmcirs.
The same type of error can result from noisy spread-function data. Hand smoothing the noisy spread-function traces will not necessarily reduce random errors in the m.t.f. without the possibility of incurring systematic errors.
REMARKS ON THE USE OF M.T.F. TO CHARACTERIZE A NON-LINEAR, NON-STATIONARY DEVICE The above restrictions on the conditions for measuring a m.t,.f. may not be satisfied in the practical application of the channel tlube. If the screen is to be examined visually, the image may be no less useful for all that it is non-linear and non-stationary. Indeed, sornetimes a non-linear response is an advantage for very high scene contrasts and is often encouraged to obtain tone compression in the highlights. I n such circumstances a tube characteristic n1.t.f. which is
600
E. C. YEADON AND J . A . CLARKE
measured in such a way in order to avoid the mathematical complexities of non-linearity and non-stationarity may not be relevant to the tube in the conditions of use. As long as a unique tube m.t.f. is required, it is essential to take all the precautions necessary to ensure validity of the result. But consideration should also be given to the intended use and, where a non-linear response is expected, it is important to use the normal subjective criteria of image-quality assessment to supplement the results of linear analysis.
REFERENCE 1. Papoulis, A., “Systems and Transforms with Applications in Optics,” McGrawHill, New York, (196s).
DISCUSSION w. L. WILCOCK: Would it not be possible to extend the frequency region in which the m.t.f. can be usefully defined by introducing lateral motion of the image tube relative to the observer, for example, by small amplitude vibrations? E. 0.YEADON : Dynamic scanning would indeed get round some of the difficulties of the sampled image. But) any movement of the image over the tube would effectively reduce the m.t.f. because of the persistence time of the phosphor screen. The form of dynamic scanning that would most improve the image would be lateral motion of the channel plate, with the image stationary on the screen. This would be impractical in such a short tube. H. BONQARTZ: Did your image intensifier have a fibre-optic plate on the photocathode side 7 It is possible that the auto-correlation functions (or radial distribution functions) of the fibre-optic plate and the channel plate have the same form but different correlation lengths. It is also possible that there is a non-zero correlation between the two plates, in which case you may not combine the m.t.f.’s. Did you find any evidence of this? E. 0.YEADON : The fibre-optic plate at the photocathode has fibres arranged on a square lattice of 7 pm pitch. This is too high a spatial frequency to be sharply imaged on the channel plate by the electron optical imaging stage, and the image formed on the channel plate is effectively continuous. We have seen no evidence at all of intorference between the square fibre-optic lattice and the hexagonal packing lattice of the channel plate. E. w. DENNISON: With reference to the imaging between the channel plate and the output screen, what difference would you oxpect betweon proximity focusing and magnetic focusing? E. c . YEADON : Magnetic focusing would be expected to improve the sharpness of the image on the screen. But proximity focusing is already good enough to resolve the individual channel spots, and any further improvement could only be marginal from the point of view of information transfer. Magnetic focusing would increase the size and weight of the tube, and there would be difficulties in isolating the electrostatic focused inverter section from the very high magnetic field which would be necessary to form the image in the space available.