R2-33 – Measurement of Laser Based Projection Displays
R2-33 – Measurement of Laser Based Projection Displays
Reporter: K. Niall (CA)
Terms of Reference: To describe concepts and methods of photometry for the comparison of laser-based projection displays.
Introduction
This Reportership addresses issues related to the luminance and contrast of an emerging class of displays: laser-based projection displays. Laser based projection systems are composed of a laser based video projector (LBVP) together with either a rear or front project screen. An LBVP, in turn, consists of laser beams that are scanned and synchronously modulated. The aim of the Reportership is to develop concepts and methods for the comparison of many different laser-based projection displays.
An important characteristic of the LBVP is the very short lifetime of the pixels. Each pixel produces light only for the very short time during which the laser beam passes over it. This means the optical signal is relatively weak and contains rapid transients. The short transients make the measurement of LBVP image’s properties more difficult to obtain in comparison to conventional display devices. Thus the validity of the characterization of LBVP images by conventional methods is questionable.
The current report is based on work conducted by Michel Doucet of INO under contract to DRDC Toronto [1]. It examines the factors that may impact the accurate measurement of laser based projection displays including the display characteristics that may interact with the measurement system and other factors that can affect measurement accuracy. Display factors include the effect of spatio-temporal factors such as pixel overlap, fill, shape, and duration. Other factors include speckle, parasitic light, reflections, and ambient illumination that can affect the correlation between the measured luminance and contrast and human perception of brightness and contrast.
Based on an assessment of these issues and how they might interact with the characteristics of radiometric measurement systems, a three step measurement method is proposed. The first step would be to measure the irradiation pattern produced by the projector in the vicinity of the normal screen position. This allows a better response from the measuring optical sensor in comparison with conventional methods due to a stronger signal. The second step would involve characterisation of the directional diffusion properties of the screen or more precisely the measurement of its bidirectional reflectance distribution function (BRDF). The third step would be to compute the illumination characteristics for any observer position from the measured irradiation pattern and the diffusion properties of the screen. The report concludes with a proposal for future work within Division 2 to further develop and validate the proposed method.
Considerations in the measurement of laser projection systems
There are several factors that must be considered in the measurement of laser projection systems. To start, it is important to consider the characteristics of the system being measured. With a projection system, this includes the characteristics of the screen as well as the projection source. In addition, it is important to examine the factors that might affect the accurate measurement of the system. An accurate measurement is one that correctly reflects what is perceived by the human visual system. Thus, additional light sources that may corrupt the measurement or the perceived output must be accounted for.
Projection screen characteristics
The projection screen receives light from the projector and redistributes it toward the audience. The rays generated by the projector and reaching a particular pixel on the screen can be considered as nearly collimated. The screen redistributes the directions of these rays and each pixel becomes a secondary source that can be seen from all positions in front of the screen. Depending on the type of screen, which can be reflective or transmissive, various physical principles can be used for the redistribution of the rays’ direction. In order to calculate the luminance of the screen, it is necessary to be able to describe their characteristics. The simplest case is for a Lambertian screen. However, very few projection screens in use today can be described as Lambertian. For the more general case, it is necessary to calculate the bidirectional reflectance distribution function (BRDF). Once the characteristics of the screen are known, it is possible to compute the screen luminance from the measured irradiance of the projector.
Lambertian reflective screen
The simplest reflective screen is a flat surface coated with a white diffusing layer (matte white paint). Some types of coatings have scattering properties very similar to a Lambertian diffuser. The case of the Lambertian screen is very interesting because the radiance of the light reflected on such a surface can be easily determined from the irradiance. The calculation for this is outlined with the help of the schema in Figure 1.
|[pic] |
|Figure 1. Radiance from a Lambertian diffuser. |
In Figure 1, δAL is a small element of the Lambertian screen, ΔAr is an annular portion of a spherical surface centered on point C of δAL and δAr is a small element of ΔAr. The sphero-annular element ΔAr is centered on axis CQ, which is perpendicular to the surface of element δAL. The flux dΦ reflected from element δAL toward the small receiver element δAr is given by the following equation:
|[pic] |(1) |
where B(θ,ϕ) is the radiance of the small element δAL toward direction CP, R is both the radius of the spherical surface and the distance between points C and P, θr is the angle between line CP and the normal to the element δAr, and dAL and dAr are the areas of elements δAL and δAr respectively. Since δAr is on the spherical surface, its normal points toward C, thus θr equals zero. Moreover, B(θ,ϕ) is constant because the surface is Lambertian. Due to symmetry, flux on any part of ΔAr is also given by equation (1), with θr equal to zero. The flux ΔΦ on ΔAr is given by:
|[pic] |(2) |
where r is the distance between points Q and P.
Adding contributions from annular sections of the sphere gives the total flux Φ reflected by the element δAL:
|[pic] |(3) |
For a Lambertian surface, light is reflected in all directions of the half sphere in front of the surface, thus the half angle u of the cone of light is 90o:
|[pic] |(4) |
The reflected flux Φ is proportional to the flux Φin incident on element δAL. The proportionality constant is called the reflectivity ρ, and takes into account the transmission and losses due to absorption. Finally, the radiance produced by a Lambertian screen is:
|[pic] |(5) |
where E = Φin/dAL is the irradiance incident on element δAL.
The Lambertian screen is an example of how the radiance of the reflected light is related to the incident irradiance on the screen. This method of computing the radiance of reflected light from the incident irradiance is not limited to Lambertian screens; in general, knowledge of the reflectivity properties of a screen enables the computation of radiance from the incident irradiance.
Reflectivity characteristics of a general screen
The reflectivity characteristics of any screen can be presented with the concept of the screen gain, or as a bidirectional reflectance distribution function (BRDF). The BRDF is a more precise and more complex representation of the reflectivity properties of materials [2], but it is a valid description only for particular types of materials.
The BRDF gives the differential reflected radiance produced by an oriented incident beam. The geometry is illustrated in Figure 2. The oriented beam is defined by the element source δAs and the reflecting element δAd. This beam produces a spectral irradiance dE(θr,ϕr,λ) on δAd. The differential spectral radiance dBr(θr,ϕr,λ) of the reflected radiation is measured by receptor element δAr.
|[pic] |
|Figure 2. Geometry for the BRDF. |
The BRDF is defined by:
|[pic] |(6) |
It is a function that characterizes the geometrical and spectral-reflectivity properties of the reflecting surface for points around the centre of the small element δAd. For elements δAs, δAd and δAr, small in comparison to the distances between them, the reflected radiance varies proportionally with the irradiance, and the ratio of these quantities varies only with the reflective properties of the small element δAd. This reflective element must be small enough to avoid non-uniform properties.The angular distribution of the radiance of some types of highly diffusing materials does not change significantly with the incident direction. For those materials, the BRDF varies only with the reflection angular coordinates, fr(θi,ϕi, θr,ϕr,λ) = fr(θr,ϕr,λ). The Lambertian diffuser belongs to this family of materials, because its radiance is constant. For Lambertian materials, the BRDF is constant, fr(θi,ϕi,θr,ϕr,λ) = fr(λ). For screens made of highly diffusing materials, the gain g(θr,ϕr,λ) is defined as the ratio of their incident direction-independent BRDF over the BRDF of a perfect Lambertian screen:
|[pic] |(7) |
If E(λ) is the total spectral irradiance on a small element for both the characterized screen and the perfect Lambertian screen (ρ = 100% at all wavelengths), the reflected spectral radiances for the two cases are:
|[pic] |(8) |
The gain is also given by:
| [pic] |(9) |
|[pic] | |
Projector characteristics
There are two primary approaches to displaying images with lasers:
a. Flying spot: This method uses a laser beam that is scanned in two orthogonal directions. The intensity of the laser beam is modulated as the spot moves on the screen. Depending on the type of laser used, the beam intensity is modulated by acting directly on the electric power supplied to the laser, or by means of an external optical modulator. An external optical modulator is the most common modulation used for high-powered lasers, and consequently, for projection displays.
b. Linear spatial light modulator (SLM): Many laser-based projector technologies make use of the deformation of a reflective microstructure to modulate the light. The microstructure deformation causes deflection[1] of the illumination beam, and modulation is accomplished by means of a blocking stop. The deformable microstructure is replicated to form a linear array of light modulators, or a linear SLM. When illuminated with a thin laser line, a linear SLM enables the display of a line of pixels. A complete image is produced by scanning the line of pixels by means of a scanning mirror.
At minimum, the proposed measurement methods should be suitable for these two types of displaying mechanism. Table 1 summarizes the principal properties characterizing a laser-based projector and the complications these properties may entail. Characterizing the luminance and contrast of these types of projectors requires a sampling process, which must be adapted to take into account the spatial distribution and the temporal fluctuations in the laser system as described above. In addition, it is important to consider the capabilities of the detectors used in the measurement process. Otherwise, the output on the screen will not correspond to the brightness and perceived contrast. The impact of these factors is expanded on in greater detail below.
Table 1. Laser projectors’ principal properties and their complications.
|Properties |Problems |Cautions |
|Laser illumination |Laser systems are subject to different types of optical|The coherent noise of the laser system generates |
| |noises not present in incoherent conventional systems. |image artifacts. The measured energy must be |
| |Any dust particles on an optical surface may cause the |integrated over a large enough portion of the image. |
| |apparition of concentric ring patterns. The speckle | |
| |phenomenon may also occur, altering the image quality. | |
|Scanning |During the scanning process, each pixel is displayed |Involves an intense flux of light for a very short |
| |for a very short period of time. Individual pixel |period of time. Care must be taken to ensure that |
| |displays are abrupt events. |measurements are representative of the energy |
| | |involved in the process. There are risks of detector |
| | |saturation, and tests must be run to control for it. |
Spatial sampling
The image produced by a video projector generally consists of a periodic arrangement of a very large number of small discrete elements called pixels. Depending on the technology used, there can be dead zones between pixels or inside each individual pixel. This periodic structure may induce measurement errors. As well, speckle noise produces a random spatial redistribution of energy that may also induce measurement errors if the spatial sampling is inadequate.
Pixel filling, pixel overlap, pixel shape
This section concerns all structured non-uniformity of the spatial distribution of energy. Figure 3 illustrates the problem of spatial sampling in the presence of structured non-uniformities, in the particular case of horizontal dead stripes between successive rows of pixels. Such a pattern is characteristic of laser-based video projectors with a linear SLM.
|[pic] |
|Figure 3. Effect of dead stripes between pixel rows on the energy measurement for different sizes of the sampled zone. |
The measurement of the image’s irradiance, or its radiance or luminance, involves spatial integration over a group of pixels. The amount of energy collected by the device depends on the zone in the image sampled by the detector’s active area. Figure 4 shows the variation in the proportion of the area occupied by dead stripes as the size of the detector is increased. The dimensions of the detector L and H, the stripes width δ and the centering parameter Δ are all normalized by the height P of the pixel. The curve in Figure 4d corresponds to a round detector, while a, b and c represent the effect obtained with a square detector. The detector is perfectly oriented with respect to the stripes (θ = 0) in the case of the first curve, while the second and the third correspond to the rotation angles θ of 45o and 40o respectively. In all cases, the normalized width ( of the stripes is 0.1. This means that 10% of each pixel is occupied by dead area. The best results are achieved with a square detector rotated by 45o with respect to the stripes. The fluctuations of the area ratio are reduced very quickly, and the curve reaches its converging value for a detector size of about 10 pixels. The result for a rotation angle of 40o is nearly as good as its counterpart with a rotation angle of 45o. This means that a square detector that is 10 pixels high, and rotated by about 45o with respect to the dead stripes, gives a measure of energy very close to the ideal case of a detector with infinite dimensions.
|a)[pic] |b)[pic] |
|c)[pic] |d)[pic] |
|Figure 4. Variation of the proportion of the dead zone as a function of the detector size. The curve located at the bottom right of |
|the figure corresponds to a circular detector while the others are for a square detector. Following the normal order, the first |
|curve corresponds to a detector perfectly oriented with the stripes, while the second and third ones are rotated respectively by 45 |
|o and 40 o with respect to the stripes. |
These results are also valid for any type of systematic non-uniformity in the energy distribution within the pixel. This includes the case of partial overlapping (flying-spot projector) and pixels with unusual shapes. The fast-convergence behaviour for the square detector rotated by 45o is valid even for a filling factor (active area/total area) as poor as 55% (curve with an asymptotic value of 0.45), as shown in Figure 5a. The amount of energy collected by the device, assuming a square detector rotated by 45°, is also insensitive to the centering of the detector with respect to the pixels, as is shown by the image in Figure 5b. Centering errors of up to +/- half of a period (Δ = P/2) do not alter the asymptotic convergence. This is true for horizontal patterns as well as vertical patterns, due to the symmetries. The good behaviour of the tilted-square detector is explained by the fact that dead zones enter or exit the detector at the detector’s corner tips, where its width is small enough to not significantly modify the energy budget.
|a)[pic] |b)[pic] |
|Figure 5. Asymptotic behaviours of the square detector rotated by 45 ° for different fill factors (a) and different centerings (Δ = |
|0.15, 0.25, 0.4, 0.5) (b). |
The size of the image produced by a video projector is generally quite large. It is not certain that large detectors, with sizes around 10 image pixels, exist. For a detector smaller than 10 image pixels, the mean value of the measurements at different positions in the image should be taken. The detector can be moved using a motorized linear displacement stage. Figure 6 shows the curve corresponding to the mean value for 50 displacements of the detector as a function of the detector size. In all cases, the detector is moved across a distance of 10 image pixels in 50 equidistant steps. As seen in this figure, the results are accurate even for detectors with a height as small as one image pixel.
|[pic] |
|Figure 6. Mean value of the ratio of dead/zones/detector are as function of detector size for a nominal ratio of 0.1, |
Temporal sampling
The scanning process in a laser-based video projector involves large transients in the optical signal. To reduce the risks of measurement error, this signal must be sampled at an adequate rate.
Detection-system bandwidth
As mentioned earlier, the lifetime of a particular pixel is very brief, but intense. A detector receiving the light of a given pixel perceives a rapid and substantial increase in luminous energy, followed by a similar, sudden decrease. Figure 7 shows the shape of the simulated signal that would be produced by a tilted square detector and a circular detector, both with infinite bandwidth. Calculations are done considering a uniform vertical line of light that is scanned over the detector at uniform speed. This corresponds to the measurement of the irradiance on the screen for a linear SLM projector. The curves give values proportional to the surface of the detector that is covered by the vertical line of light proportional to the instantaneous optical power on the detector. For a detector operating in its linear range of operation, the produced electrical signal should take a shape similar to the curves shown in Figure 7.
Consider the case of a linear SLM projector producing an image with 1280 by 1024 pixels, and a refreshing rate of 60 hertz (Hz). If we can disregard the loss of time between two successive frames, the generation of an entire image takes 1/60 of a second. Suppose that the irradiance of this image is measured with a 45o-tilted square detector with sides measuring 10 pixels. The diagonal of such a detector measures 14.14 pixels, thus the pulse produced by the scanned line lasts about [(14.14+1)/1280](1/60 sec.) = 197 μs. The detector receives only parasitic light for the rest of the frame period, about 16.47 ms. The measurement of the energy of such an optical signal must be done using a fast-calibrating photometer capable of taking optical-signal samples at each 2 to 10 μs interval. The other possibility is to capture the signal of a rapid photodetector with a fast digital oscilloscope and to multiply the values using appropriate conversion factors. This would require a calibration process to determine the precise values of the multiplying factors.
|[pic] |[pic] |
|a)[pic] |b)[pic] |
|Figure 7. Simulated peak shape in the case of the scanned linear SLM projector respectively for a 45° tilted square detector and a |
|circular detector. |
The transimpedance circuit configuration is commonly used for the amplification of the signal produced by a photodiode. The equivalent circuit is shown in Figure 8. The simplified model of the photodiode is a current source Sc in parallel with a capacitance C and a resistance R. The photodiode is polarized with a reverse-bias voltage V. The amplification is provided by an operational amplifier (Op-Amp) with an open loop voltage gain G. Choosing the value of the gain G >> 1 and the values of the feedback resistance Rf, such that RG >> Rf, , the frequency response of the output voltage Vo is given by Iizuka [3]) (equation (10)).
|[pic] |
|Figure 8. Equivalent circuit of the detection device. |
|[pic] |(10) |
where i is the current flowing through the photodiode, f is the frequency of the signal and fc is the cutoff frequency of the circuit. We have:
|[pic] |(11) |
Equation (11) is proportional to the transfer function H (f) of the system. The dynamic response of the amplified detector is given by the convolution of the input signal with the impulse response h(t), which corresponds to the response of the system to a Dirac delta impulse. The transfer function and the impulse response are a Fourier transform (TF)-pair [4].
|[pic] |(12) |
|[pic] | |
Considering that the current i consists of a constant component plus a component proportional to the optical power, the output signal of the amplified photodetector consists of a bias plus a signal that follows the optical signal. We consider only the component Vop of the signal Vo that depends on the optical signal, because the bias component is a constant that can be removed. Vop is determined by computing the convolution of the optical signal x(t) with the impulse response h(t). The curves in Figure 7 give x(t). Those curves can be approximated by a sum of Gaussians. Using this fit, an analytic solution to the convolution can be obtained:
|[pic][pic] |(13) |
where:
|[pic] |(14) |
The signals x(t) of Figure 7 are analytical functions as well as the computed responses of the detector.
Figure 9 shows the simulated responses for an amplified reverse-biased photodiode detector with different cutoff frequencies. Figure 9a, b and c correspond to a square detector tilted by 45o, with cutoff frequencies of 5 kHz, 10 kHz and 25 kHz, respectively. Figure 9d is for a circular detector with a 25 kHz cutoff frequency. All the results shown in Figure 9 concern a square detector with 10-pixel sides, or a circular detector with a 10-pixel diameter.
Figure 9 compares the simulated response with the response generated by the same detector shape, but with an infinite cutoff frequency (perfect detector). A cutoff frequency of 25 kHz seems to be enough to obtain a detector signal that is similar to the optical signal. The circular detector presents a response similar to a tilted square detector.
|a)[pic] |b)[pic] |
|c)[pic] |d)[pic] |
|Figure 9. Simulated response of a tilted square detector with three different cutoff frequencies, and a circular detector. |
The relative size of the detector with respect to the laser-line width has an impact on the dynamic response of the detector. Figure 10 shows a tilted square detector with 2-pixel sides instead of 10. We can see that if the size of the detector is reduced, the cutoff frequency must be increased to maintain the same level of fidelity between the simulated response and that of a perfect detector . Figure 10a corresponds to a 25 kHz cutoff frequency, while Figure 10b is for a 50 kHz cutoff frequency. It seems that a significant increase (a factor of 2 to 3) in the cutoff frequency is required for a 2-pixel wide detector to achieve the same performance as a detector five times that size.
|a)[pic] |b)[pic] |
|Figure 10. Simulated response in a linear SLM projector for a tilted square detector with 2-pixel sides. |
In the case of the flying-spot, laser-based video projector, a much faster detection device is required. Figure 11 shows the simulations for the same image format and frame rate as considered in the previous cases. Figure 11a and b correspond to a 10-pixel high square detector with cutoff frequencies of 10 MHz and 50 MHz respectively, while c and d are for a 2-pixel high square detector with, respectively, 50 MHz and 90 MHz cutoff frequencies.
|a)[pic] |b)[pic] |
|c)[pic] |d)[pic] |
|Figure 11. Simulated response in a flying spot, laser based video projector for a tilted square detector with 2-pixel sides. |
Sampling rate
In the case of the linear SLM projector, it is conceivable to use a fast calibrated detector, coupled with a digital oscilloscope, for the acquisition of the signal. A cutoff frequency of about:
|[pic] |(15) |
is probably enough for the detection system (photodiode plus amplifier), where N is the number of pixels in the scan direction, Fr is the frame rate in Hz and nd is the size of the detector measured in number of pixels along the scanning direction. Once the signal is digitized, it is multiplied by the calibration factor to convert it into the corresponding instantaneous optical power. The energy in the optical signal is computed by numerical integration of the optical instantaneous power signal. The mean value of the irradiance over one frame period is obtained by dividing the energy by the detector area and the time period of a frame. Considering that about 100 samples are probably enough to accurately evaluate the energy contained in the pulse, an approximate value for the sampling rate Sr can be estimated as:
|[pic] |(16) |
In the case of a 60 Hz frame rate with a resolution 1280 by 1024 pixels, a sampling rate of 2.56 x 106 samples/second would be required for a detector measuring only 2 pixels. This is within the reach of modern digital oscilloscopes, which have sampling rates of several tens-of-million samples per second, or more.
The phenomena involved in a flying-spot projector are thousands of times faster than those for a linear SLM, and a specific measurement strategy must be used. The optical signal is a short pulse followed by a long, slow varying plateau. The pulse is similar in duration and intensity to the signal produced by a pulsed laser. Special detectors exist for such pulsed lasers. These detectors directly measure the energy contained in the laser short pulse. However, such detectors cannot measure a long pulse, or slow varying optical signal. The idea is to combine a pulse detector with a photodetector. The two detectors are placed, one after the other, along the scanning direction. The pulse detector measures the energy of the pulse while the photodetector measures the mean energy between pulses in the manner describes in the previous paragraph. For this application, a few hundred samples are sufficient for the acquisition of the plateau signal. A photodetector with a cutoff frequency around 1000 Hz and a sampling rate around 10,000 to 20,000 samples per second would probably be sufficient.
Speckle ……..
Speckle occurs when the wavefront of a coherent beam is randomly modified [5]. For example, this can happen when a laser beam is reflected on, or transmitted through, an uneven surface. These conditions are encountered when an image is projected by a laser-based video projector and reflected by a diffusing screen. Due to time averaging, the speckle is greatly attenuated because the scanning process produces fast modifications of the speckle pattern. However, setting aside its effects on image quality, speckle can cause measurement error if the speckle grains are not small enough in comparison to the size of the detector.
Figure 12 shows the process of speckle generation when the laser beam is reflected on the screen, in the particular case where the diffusing properties of the screen are due to microtopography. The eye of the observer is modelled by a simple lens, and the eye-equivalent system is compared with a high-performance optical system. Both systems make an image of the illuminated part of the screen. The small diffusing sites on the screen are not resolved by the optics of the eye and the optical path difference of rays coming from an area larger than the surface features will result in the eye seeing a speckle pattern. The resolution of the high-performance system is supposedly significantly better than the mean size of the diffusing sites. The small surface features will be seen in enough detail by the high performance system, resulting in a negligible optical path difference for rays coming from an area smaller than the surface features and thus no visible speckle pattern.
|[pic] |
|Figure 12. Process for the formation of a speckle pattern. The small images on the right correspond to a zoom in on a small portion|
|of the image plane. |
In the case of a high-performance system, the rays associated with a given point on the image plane are in synchronicity and interfere constructively. This comes from the Fermat principle, which stipulates that all possible optical paths from an object point to its image are equal. For a high-performance optical system, the rays that reach a given point in the image plane come from roughly the same object point and follow the Fermat principle. Moreover, the region on the object that reflects rays toward the considered image point is small enough to be considered flat. The situation is different in the case of the human visual system. The rays that illuminate a given point on the retina come from a small zone on the screen containing many tiny bumps. The microtopography of the surface induces random variations in the optical path of the incident coherent rays. As a result, the rays are no longer synchronized when they arrive at their common point on the retina. The intensity at this point is the result of the interference of all those rays. Hence, it is the statistics on the optical-path lengths that determine the intensity of the image point.
The set of rays associated with another image point has a different optical-paths distribution and the interference may result in a totally different value of intensity. Depending on the roughness of the surface and the resolution of the optical system, the characteristics of the image can vary between those of a perfect image and those of a highly contrasted, grainy pattern. The more the speckle pattern is developed, the more its intensity distribution is sensitive to small variations of the optical configuration. A small displacement of the diffusing surface, or a small change in the angle of incidence of the beam, changes the sets of rays that converge to the considered image points. This may cause the formation of a totally different speckle pattern. Due to the scanning process, the image produced by a laser-based video projector appears to the observer as the superposition of many, slightly different, speckle patterns. This process considerably reduces the image’s noisy appearance.
As for other interference phenomena, there is no creation or annihilation of energy, only a redistribution of the incident energy. The energy integration in a portion of the image containing a large number of speckle grains is representative of the mean energy incident on the corresponding part in the object plane.
In an image produced by a laser-based video projector, the speckle is generated when the light is diffusely reflected by the screen. Speckle patterns are unlikely to occur in the optical path preceding the screen, because the optical surfaces that comprise the projector do not have scattering properties. The problem of speckle is significant only for the measurements done with a telephotometer after reflection on the screen. For such measurements, one must ascertain that the observed zone contains a large number of speckle grains. In measuring image intensity before reflection from the screen, the speckle phenomenon does not need to be taken into consideration.
Parasitic light
The brightness and contrast of an image projected by a laser-based video projector onto a screen depend primarily on the power of the projector’s laser sources and the switching characteristics of the light modulators. The brightness and contrast perceived by the observer and/or measured by a radiance or irradiance meter, on the other hand, can be affected by other sources of light. In determining perceived brightness, it is important to determine the impact of these sources of light on the measured and the perceived output.
Some types of parasitic light are intrinsic to the projector and depend on the quality of the optical components used in its construction. Unfortunately, intrinsic parasitic light may depend on the spatial intensity distribution of the displayed image. Other types of parasitic light originate in the environment, and can vary significantly between locations. These sources are not specific to laser-based video projectors, and can affect the performance of traditional projectors. The most important sources of parasitic light are:
• veiling glare produced by reflection on the components of the projection optics
• reflections back to the projection screen
• ambient illumination
• stray light in the observing device
Veiling glare is intrinsic to the projector, while reflections and ambient illumination depend on the characteristics of the room where the projection takes place. In general the effect of extraneous light sources that impact on the measured output and not the perceived output, such as stray light, should be minimized during the measurement process or assessed and deducted from the measurement process [6]. The impact of stray light is generally minor when the observing device is the human visual system, but can be significant when observed by a camera or light measuring device (LMD) equipped with a lens. The effect of light sources that affect both perceived and measured output, such as ambient illumination, should be calculated separately since they tend to vary over time and location of the projection system. The following paragraphs give a more detailed description of these sources of parasitic light affecting the quality of a projected image. Methods for reducing many of the negative effects of parasitic light when measuring contrast can be found in a series of papers by Boynton and Kelly [6-8].
Veiling glare
Despite technical progress in optical anti-reflection (AR) coating, there is still non-null reflection at the glass interfaces. The most severe problem occurs in complex optical systems that contain large numbers of lenses, as a part of the light reflected on lens interfaces is transmitted toward the screen. This parasitic light is called veiling glare. Veiling-glare light also includes specular and diffuse reflections of light by the mechanical parts of the lens.
The amount of veiling-glare light increases with the intensity of the beam passing through the optical channel. It can be reasonably supposed that the principle of superposition applies; the veiling-glare phenomenon can thus be represented by a linear equation, according to Badano and Flynn [9]. Moreover, if the properties of the AR coating are uniform over lens surfaces, it is reasonable to presume that veiling glare is not greatly dependent on image-intensity distribution.
Veiling glare is intrinsic to the projector, but depends on the amount of light passing through the optics and the amount of light projected on the screen. It is important to select the image used in measurements to include a representative amount of parasitic light from the veiling-glare process. Illuminating only the small portion of the screen where measurements are made has the advantage of reducing parasitic light, such as that caused by veiling glare. However, such a low level of veiling-glare light is not representative of normal operating conditions, and leads to overestimations of contrast value.
Back reflection
The purpose of the projection screen is to diffuse light coming from the projector toward the observers. Unfortunately, the light diffused by the projection screen not only illuminates observers’ eyes, but also the projection-room walls and objects within the room. These objects, in turn, diffuse the light throughout the room, including back to the screen. This back-reflected light can significantly reduce the contrast of the projected image by producing background illumination. The amount of light reflected back to the screen depends on the configuration of the room, and the absorption and reflection characteristics of the walls and objects. The resulting image brightness, and especially the contrast, can differ significantly from one room to another. The amount of back-reflected light can be evaluated using simple techniques (see the Proposed measurement method section, General description, Reduction of measurement errors due to parasitic light).
Ambient illumination
In a manner similar to back reflection, ambient illumination reduces the contrast of a projected image by way of background illumination. With a high level of ambient illumination, the screen can appear white even when the projector displays a black image. Contrast reduction is less severe for high-powered projectors. Ambient illumination may come from light passing through curtains or under doors. It may also come from any source of light inside the room, such as computer screens or illuminated signs.
Stray light in the observing device
The radiometric features of an image displayed on a screen may be measured by means of an imaging device. A lens is used to produce an image (a replica) of the intensity distribution displayed on the screen, and the radiometric features of this image are used to calculate the radiometric features of the image displayed on the screen. Such an approach has an intrinsic limitation, because reflection and diffusion occur on the optical and mechanical parts of the lens, the level of fidelity of the image displayed in the image plane of the measurement device is reduced. Stray light can even come from areas located outside the observed zone. An extreme example illustrating this kind of degradation is the capture of outdoor photographs on a very sunny day. When rays of the sun illuminate the first lens and the mechanical supports, veils of light appear and can considerably reduce the contrast of the pictures. In imaging devices, stray light can cause portions of the screen to appear more luminous to the measurement system than they really are, causing considerable errors in the evaluation of brightness and contrast.
Proposed measurement method
This section describes the proposed method for measuring the luminance and contrast of a screen image projected by a laser-based video projector. Existing methods [10] for measuring projection screens involves either the direct measurement of luminance and contrast for back projection systems or the calculation of luminance from the measurement of illuminance for front projection systems. However, interactions between the laser pulses and the screen make direct measurement problematic even for back projection systems. Thus the proposed method builds on the current method for front project systems and recommends its use with all forms of laser based video projection systems. It involves three characterization steps. First, the irradiance is measured at a plane before the screen. Second, the screen’s BRDF is characterized. Finally, the luminance is computed for any observer position, using the measured irradiance pattern produced by the projector at the screen position and the screen BRDF.
Step 1: Measurement of irradiance
In the first step of the proposed method, the irradiance is measured at different points in the plane or the surface located immediately in front of the screen. To minimize back reflection from the surrounding environment, replacing the screen with a black absorbing curtain is recommended. The test pattern proposed for the measurements is a 10 by 10 chessboard containing 50 dark squares and 50 bright squares. The irradiance measurements are taken in the middle of each bright square. For each sampling position, a first measurement is taken to obtain the maximum value of irradiance; from a reverse video test pattern, a second measurement is taken to obtain the minimum value.
Detector characterization
Prior to making measurements, the response time of the detector must be determined to ensure it is fast enough. A setup similar to the one in Figure 13, consisting of a laser and a rotary scanning mirror, can be used to evaluate the response time of the sensor. An attenuation filter is used to obtain optical power comparable to the expected power for the small region of the image corresponding to the detector area. The laser is focused on the surface of the slit placed in front of the detector. As the mirror is rotating, the focused spot passes periodically over the slit and the corresponding peak can be seen on an oscilloscope. The response time may be evaluated by measuring the rise and fall time of the peak signal. This must be done at both a slow and a fast rotation speed. The slow rotation speed enables evaluating the part of the rise and fall times due to the finite size of the laser spot.
If a fast power meter or energy meter is available, there is probably no need to perform any tests before proceeding to the measurements.
|[pic] |
|Figure 13. Optical setup for detector response-time evaluation. |
Detector saturation
Detector saturation should also be assessed prior to making measurements. As indicated in Table 1, the intense brief pulses that are characteristic of flying-spot laser projectors, can saturate the detectors found in light measuring devices such as telephotometers, radiometers, illuminance, and irradiance meters. The result will be a noticeable difference in the perceived versus the measured output. The problem may be circumvented though the use of the use of special detectors designed for laser pulses coupled with a photodetector. However, even with these types of systems, it is important to verify that the laser pulses are not saturating the measurement device. Diagnostic techniques to check for detector saturation and its possible causes are described by Boynton and Kelly [11, 12]. Their basic method involves comparing the brightness of a conventional display source such as a Cathode Ray Tube (CRT) with the brightness of the laser projection system screen. Initially, observers must adjust the output of the conventional system until it appears as bright as the laser based projection system. Once the two systems appear equally bright, the light measuring device can be used to assess their luminance or illuminance. If there is a significant difference in the measured output, it is likely that the pulse from the laser projector is saturating the detector.
Once a mismatch has been identified, further tests are possible to identify the source of the mismatch. These are also described by Boynton, et al. [11, 12] along with examples of how they might be employed in the evaluation of laser-display systems.
Test pattern
The proposed test pattern consists of the 10 by 10 chessboard represented in Figure 14. As can be seen, half of the screen is at the lowest value of the grey scale, while the rest is at the maximum value. This provides about half the total optical power that can be produced by the projector and a representative amount of intensity-dependent intrinsic parasitic light (veiling glare, etc.). Measurements are done at the center of the bright squares. The magnification factor should be adjusted so that each chessboard square is at least twice as large as the detector to avoid edge effects. The maximum values of the optical irradiance are measured at the center of the bright squares, while the minimum values are measured at the same positions, but with the video inverse pattern. Using an image with smooth transitions between adjacent dark and bright regions is recommended to eliminate high-spatial frequencies and avoid image aliasing.
|[pic] |
|Figure 14. Test patterns. The pattern on the right is the video inverse of the left pattern. |
Detector shapes and sizes
As mentioned previously, a tilted square detector presents very interesting behaviours with regard to spatial sampling. A detector with side dimensions measuring at least 10 pixels is recommended. The magnification factor of the test pattern may be adjusted appropriately to fulfil the 10-pixel criteria. However, one must keep in mind that the distance between the projector and the screen has to be large in comparison to the diameter of the exit pupil of the projector. This is required for the validity of the calculation with the BRDF (see Determining spectral radiance of a screen from its BRDF). If a square detector is not available, a round detector is also acceptable, provided that its diameter and magnification factor are such that the area perceived by the sensor is at least 15-pixels wide. For both types of detectors, the centering with respect to the pixel is not critical. For the tilted square detector, the tolerance range for the orientation is about +/- 5°; this degree of accuracy can be achieved without the help of an instrument.
Usually it will not be possible to find a detector that is both fast enough and large enough to fulfill the 10- or 15-pixels criteria. In that case, the detector must be shifted over a minimum 10-pixel size area of the image and the mean value over a large set of positions (approximately 50) must be taken, as explained in the Spatial scanning section.
Detector-system cutoff frequency and sampling rate
In the case of the linear SLM projector, a detector cutoff frequency of about:
|[pic] |(17) |
is probably enough, N being the number of pixels in the scan direction, Fr the frame rate and nd the size in pixels of the detector along the scanning direction. For this type of projector, a sampling rate of the detector signal given by:
|[pic] |(18) |
would probably be enough.
In the case of the flying-spot projector, a cascade of two detectors would be more appropriate for measuring. The two detectors are placed close to each other along a common scanning line (in the middle of the same square of the chessboard pattern). The first detector is a pulse detector used to measure the energy contained in the pulse part of the optical signal, while the other one is a photodetector used to measure the mean energy in the rest of the signal. Photodetector cutoff frequencies in the 100 to 1,000 Hz range and sampling rates in the 10 to 20 kHz range would be probably enough.
Examples of recommended detection devices
Table 2 shows some examples of detection systems that could be considered for doing the measurements.
Table 2. Detection-device suggestions.
|Type |Application |Supplier |Part no. |Basic characteristics |
|Fast photo-detector|Linear SLM projector |Gigahertz-Optik |MD-37-SU100-1 |Type: Si-Photodiode |
|and instrument | | | |Size: 10 mm x 10 mm |
|amplifier | | | |Spectral range : 190 to 1100 nm |
| | | | |Calibration: Spectral irradiance |
| | | | |sensitivity |
| | | |P-9202-4 |Type: Fast photodiode amplifier |
| | | | |Voltage bias: - 5V |
| | | | |Bandwidth: 330 kHz |
| | | | |Slew rate: 1 μs |
|Pulse energy meter |Pulse energy measurement, |Coherent |J3S-10 |Energy range: 0.2 pJ to 0.2 μJ |
| |flying spot projector | | |Spectral range: 190 to 1 100 nm |
| | | | |Maximum repetition rate: 400 Hz |
|Fast calibrated |Flying spot projector |Newport |1935-C |Power range: 0.25 nW to 40 W |
|power and energy | | | |Bandwidth: 170 kHz |
|meter | | | |Sampling rate: 250 kHz |
| | | | |Storage buffer: 250 000 points |
Spectral measurements
Luminance measurement requires each spectral component to be weighted by the corresponding spectral response of the human visual system. For the proposed method, this involves isolating and analyzing each individual laser line separately. For this purpose, interferential filters[2] optimized for each laser line are recommended. The transmission of each filter must be measured using a precision spectrometer. It is important that the filters have high rejection properties (optical density[3] ≥ 4) for the spectral regions outside their respective waveband. The filters must be placed near the detector, but oriented to reflect light toward the projector (normal incidence). For maximum efficiency, placing the filters in a rotating wheel enables rapid filter substitutions.
Reduction of measurement errors due to parasitic light
As mentioned in preceding sections, back reflection and ambient illumination can affect image brightness and contrast. Such signal contamination changes from place to place, posing a problem for standard measurement. Fortunately, simple techniques exist to overcome such problems. The contribution of parasitic light may be measured, and then subtracted from the useful signal. This is done by putting the detector in the shadow of a black-opaque mask. The light from the projector (including veiling-glare light) is blocked, and only parasitic light can reach it, as explained in Boynton and Kelley [7] and illustrated in Figure 15.
|[pic] |
|Figure 15. Measuring parasitic light. |
Step 2: Measurement of the projection screen BRDF
The second step is to measure the BRDF of the projection screen. The process for measuring the BRDF of projection screens is well understood. Thus, a detailed description will not be given here. Moreover, development of the necessary equipment would require significant effort.
Step 3: Calculation of luminance and contrast
Having determined the BRDF of the screen and a sampling of the screen irradiance, the luminance and contrast can be determined for any observer position and any point on the screen and the equations described below. First the spectral irradiance is computed. Second, the luminance is computed by weighting the measurements for each individual projector laser line by the appropriate spectral sensitivity curve. The contrast is computed from the luminances at the maximum and minimum output. A computer program (a MATLAB® function would do the job), can be useful in calculating luminance and contrast, and performing fits and interpolations of the BRDF data. It can also be used to easily and rapidly explore the results for many different observer positions, and produce result maps and figures.
Determining spectral radiance of a screen from its BRDF
A projector that illuminates a screen can be considered as a small element source because the screen is normally located at a large distance from the projector. Thus, we have the same geometry as in Figure 2, with the exit pupil PE of the projector objective acting as the source. This is represented in Figure 16. A small part, δAscreen, of the screen is considered and the observer is replaced by a receiving element δAr. The element δAscreen is large enough to contain a large number of image pixels, but is small in comparison to the screen dimensions and the distance DPS between the screen and the projector. The receiving surface has to be located at a large distance from the screen, in comparison to the size of the element δAscreen.
|[pic] |
|Figure 16. Geometry for computing the radiance reflected by a screen. |
Figure 16 illustrates the general case of a curved screen. The element δAscreen is localized with the position vector [pic], while the vector [pic] gives the position of the receiving element δAr. These two vectors have their origin at O and their ending points are B and C, respectively. The angular coordinates used for the measurement of the BRDF of the screen reflective material are referenced with respect to the normal [pic] of the surface, and with respect to a preferential direction defined by the unit vector [pic]. This preferential direction may be chosen, for example, along oriented microstructures devised to reflect light preferentially in a given direction. Usually, [pic]will be along the vertical or the horizontal direction.
For simplicity, the optical axis of the projector points toward the center of the screen, where the origin O of the coordinate system is located. The optical axis coincides with the z-axis, which is along the normal to the screen at point O. The y-axis is oriented in the vertical direction.
The spectral radiance Br(θr,ϕr,λ) perceived by the receiver element δAr is obtained by an integral sum over the source. The source is divided into a set of non-overlapping small source elements (As with uniform radiant properties. Using equation (5), the spectral radiance is given by:
|[pic] |(19) |
where dBr(θr,ϕr,λ)|δAs is the spectral radiance reflected by δAscreen toward δAr, but contributed by the small source element δAs alone. The angular coordinates θi, ϕi, θr and ϕr are defined as in Figure 16, except that the ϕ are measured with respect to the preferential direction defined by the unit vector [pic]. Because the exit pupil is small in comparison to the distance DPS, the angles θi and ϕi do not vary much over the elements (As of the exit pupil. Moreover, the BRDF varies slowly with the incidence angular coordinates, and all elements of the source are associated with approximately the same value of BRDF[4]. In these conditions, the BRDF within the integral may be replaced by a mean value:
|[pic] |(20) |
where [pic] are the angular coordinates corresponding to the central point A of the exit pupil, and E(xB,yB,λ) is the total spectral irradiance at the central point B of the reflecting element δAscreen. The radiance is obtained by a simple multiplication of the BRDF and the irradiance produced by the projector.
To complete the computation of the radiance, general expressions for the angular coordinates of lines AB and BC must be determined. Let (xB,yB,zB) and (xC,yC,zC) be the coordinates of points B and C respectively. The unit vectors [pic] and [pic] along lines AB and BC respectively are given by:
|[pic] |(21) |
The components [pic] and [pic], of the unit vector [pic], that are respectively perpendicular and parallel to the plane of element δAscreen, are given by:
|[pic] |(22) |
where [pic] is the scalar product of the two unit vectors. This gives the equations for the angular coordinates for incident direction:
|[pic] |(23) |
|[pic] | |
where [pic] is the unit vector along the preferential direction, and [pic] is the module of the component [pic]. Similarly, we have for the reflection angular coordinates:
|[pic] |(24) |
Determining reflected luminance
In general, the luminance L(P,D) for the point P and sight direction D can be evaluated from the spectral radiance using the following equation:
|[pic] |(25) |
where V(λ) is the normalized spectral-efficiency function of the human visual system, K is a scaling factor and dλ is the width of the waveband considered. The spectral reflected radiance is given by equation (20). Using those two equations, the luminance of point (xB,yB) of the screen, for an observer located at point (xc,yc,zc), is given by:
|[pic] |(26) |
|[pic] | |
In the case of a laser-based projector, the spectral content of the source consists of a finite number of very narrow bands corresponding to the individual narrow laser lines[5]. For such laser projectors, equation (26) is reduced to a simple sum:
|[pic] |(27) |
where Eq(xB,yB) is the irradiance at point (xB,yB) of the screen due to the qth laser with central wavelength λq.
Determining contrast ratio of the screen
The contrast ratio Cr of a point (xB,yB) on the screen is given by:
|[pic] |(28) |
Using equation (27) in equation (28), the contrast ratio can be calculated from the BRDF as follows:
|[pic] |(29) |
where Eq max(xB,yB) and Eq min(xB,yB) are respectively the maximum and minimum values of the range of irradiance that can be produced at point (xB,yB) by the qth laser line of the projector. In the case where the reflection properties of the screen do not change significantly with the wavelength (a perfectly white, or grey, screen), the equation is greatly simplified:
|[pic] |(30) |
|[pic] | |
where Lamax(xB,yB) and Lamin(xB,yB) designate, respectively, the maximum and minimum values of the luminance at point (xB,yB) for a common arbitrary direction of observation.
Conclusions and recommendations
The procedure described in this report is based largely on theoretical considerations and needs to be validated to determine that it provides a better assessment of brightness and perceived contrast than the methods currently used to measure displays. The following steps are recommended:
1. The report should be reviewed by Division 2 and feedback provided on the proposal.
2. If the proposed method and supporting material documented in this report seems reasonable, consideration should be given to implementing a Technical Committee to further develop the method and assessing it with actual laser projection systems.
3. The results of the measurement method should be compared with the results of conventional photometry and human perception of the brightness and perceived contrast of the projection systems.
While the first two recommendations fall within the mandate of Division 2, the third probably falls more within the mandate of Division 1. Thus consideration should be given to a joint Technical Committee.
References ……..
[1] Doucet, M. and Niall, K. (2008), Photometric standards for laser projectors. Luminance and contrast measurements of images projected by laser-based video projectors, (Draft), Defence R&D Canada – Toronto, Toronto.
[2] Nicodemus, F. E. (1965), Directional reflectance and emissivity of an opaque surface, Applied Optics, 4 (7), 767-773.
[3] Iizuka, K. (2002), Elements of Photonics, Vol. 2, Wiley Series in Pure and Applied Optics, B. E. A. Saleh (Ed.), New York: Wiley-Interscience.
[4] Van Den Enden, A. W. and Verhoeckx, N. A. (1992), Traitement numérique du signal, Paris: Masson.
[5] Trisnadi, J. I. (2002), Speckle contrast reduction in laser projection displays, Projection Displays VIII, Proceedings of the SPIE, Vol. 4657, 131-137.
[6] Boynton, P. A. and Kelley, E. F. (1999), Stray light elimination in making projection display measurements, Proceedings of the SPIE, 3636, 232-239.
[7] Boynton, P. A. and Kelley, E. F. (2001), Compensation for stray light in projection display technology, SID Symposium Digest of Technical Papers, 334-337 Society for Information Display.
[8] Boynton, P. A. and Kelley, E. F. (2002), Stray light compensation in small area contrast measurements of projection displays, Proceedings of the SPIE, 4657, 122-130.
[9] Badano, A. and Flynn, M. J. (2000), Method for measuring veiling glare in high performance display devices, Applied Optics, 39 (13), 2059-2066.
[10] Keller, P. A. (1997), Electronic display measurement: Concepts, techniques, and instrumentation, New York, NY: John Wiley & Sons, Inc.
[11] Boynton, P. A., Kelley, E. F., Highnote, S., and Hurtado, R. (2000), Diagnostics for light measuring devices in flying-spot display measurements, Proceedings of the SPIE, 3954, 42-51.
[12] Boynton, P. A. and Kelley, E. F. (2001), Light measuring device diagnostics for the photometric and colorimetric measurement of flying-spot displays, Proceedings of the SPIE, 4295, 235-247.
-----------------------
[1] By deviation of the beam on a tilted mirror, or by diffraction-grating effect.
[2] If the lasers may be shut down or blocked, there is no need for interferential filters.
[3] The optical density OD = -log10(T) where is the transmission T = intensity out/ intensity in.
[4] A material with rapid BRDF variation is not a good material for a screen because it will produce undesirable variations in brightness from one region of the screen to the next.
[5] Contrary to popular belief, the radiation produced by a laser is not absolutely monochromatic. Many phenomena are responsible for this fact. For example, fast molecular movements in a gas laser produce spectral broadening of the laser radiation due to the Doppler effect.
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