We present a standardized procedure to measure the amount of speckle in laser based projection systems. The parameters of the measurement procedure are chosen such that the measured speckle contrast values are in correspondence with the subjective speckle perception of a human observer, independent of the particularities of the laser projector’s illumination configuration. The resulting measurement configuration consists of a single digital image sensor in combination with a camera lens of which the settings are related to the human eye. In addition, a standardized measurement procedure and speckle pattern analysis method are suggested. Finally, the speckle measurement set-up is applied to a laser projection system and corresponding subjective speckle perception results of a large test public are discussed.
© 2012 Optical Society of America
Laser-based displays have been investigated over the past 50 years, but their applicability was limited due to the large size and high cost of laser sources [1–3]. Recent developments in visible laser technology, such as green diode lasers , are expected to give extra momentum to the development of laser-based displays. The interest in laser-based displays is spurred by the advantages offered by lasers as compared to other light sources, such as extended color gamut, small étendue and long lifetime. Unfortunately, the use of laser sources in projection applications is hampered by the emergence of laser speckle. A speckle pattern is created by interference of (at least partially) coherent radiation that is scattered from a random surface that is rough on the scale of the optical wavelength . Speckle is observed as a granular pattern on the projection screen and as such masks the depicted information. Thus, speckle has to be reduced.
Many methods to reduce speckle are based on the principle of superimposing partly decor-related or fully uncorrelated, statistically independent speckle patterns. Both instantaneous and time-sequential speckle reduction methods have been proposed. These can be divided into four different categories depending on how the superimposed speckle patterns are mutually decor-related . These four categories are wavelength decorrelation, spatial decorrelation, angular decorrelation and scrambling techniques.
When employing these speckle reduction techniques, it is essential to know how different methods influence the speckle perceived by a human being. This task is at present complicated by two factors. First of all, there is no standardized way to measure speckle. Speckle can be quantified by its speckle contrast value, , where the numerator is the standard deviation of the intensity fluctuation and the denominator is the mean intensity. This value lies between 0 and 1. For images with a small influence of speckle, this value is close to 0. Speckle patterns are often divided into objective and subjective speckle. Speckle patterns are called objective when there is no imaging involved. The speckle distribution can then be measured by for example an optical sensor without a lens. When an imaging system is involved in the formation of the speckle pattern (e.g. the speckle pattern on the human retina formed by the eye lens), we speak about subjective speckle. In this paper, focus will be directed to the latter because we wish to correlate the speckle measurement to the speckle perception of a human being. In case of a subjective speckle measurement, the configuration of the imaging set-up exerts a large influence on the measured speckle contrast . Thus, two speckle contrast values measured using different setups can not be readily compared. In this paper, we will identify and investigate the setup parameters affecting the measured speckle contrast. We will choose these parameters such that the calculated speckle contrast value is in correspondence with the subjective speckle perception of a human observer. This means that the resulting measurement configuration should yield the same speckle contrast values for different laser projector configurations if a human judges the speckle effect to be the same.
A second complication when determining the amount of speckle reduction needed in a projection system is the lack of human perception tests. In 2008, a subjective speckle perception test was performed on two test subjects . The main findings of that research deal with the optimum physical values of luminance and viewing distance for the perception of speckle. In this paper, we complement a standardized measurement procedure with human perception tests of speckle for indoor theater viewing conditions. The obtained psychophysical results are related to the proposed speckle contrast measurement as a proof of concept.
In Section 2, the relevant measurement parameters are identified and described in detail. Section 3 focuses on the standardized measurement configuration and the analysis of the speckle pattern. In Section 4, the measurement set-up is applied to a laser projection system and corresponding subjective speckle perception results of a large test public are discussed. Section 5 will summarize the results and elaborate on a possible outlook.
2. Measurement parameters
As the measured speckle contrast strongly depends on the experimental setup, we first investigate and discuss the influence of each of the measurement configuration parameters. We will look into the influence of the detection camera’s pixel area and integration time, the specifications of the camera lens and the position of the measurement system.
2.1. Experimental set-up
The experimental setup that is used to investigate the influence of the measurement parameters is depicted in Fig. 1. It consists of a single-mode (SM) laser light source with a center wavelength of 532 nm in combination with a rotating diffuser (120 GRIT polish). The latter produces a continuous variation of the speckle pattern in the projected light . Behind the diffuser, a rectangular light pipe is placed in order to obtain a homogeneous rectangular spatial light distribution. A projection lens with an f-number of 2.5 images the end of the light pipe onto a projection screen. The resulting speckle pattern is measured in reflection using a camera lens with a focal length of 30 – 70 mm and a variable f-number that ranges from f/3.3 to f/22. The camera images the projection screen on a single CCD sensor. The latter contains 1600×1200 pixels with a pixel area of 4.40 × 4.40μm2. In case unsuppressed speckle is investigated, the rotating diffuser is kept still such that the coherence of the laser beam is not reduced. Printing paper is used as the projection screen.
2.2. Clear aperture of the camera lens
The clear aperture is an important property of an imaging system since it determines the angular resolution when considering diffraction limited systems. In the case of a circular aperture, the angular resolution can be found as
As a consequence, the clear aperture of the measurement configuration determines the possible speckle reduction that can be obtained by spatial decorrelation of the projected light. For example, in case of the projection configuration with the rotating diffuser, the solid-angle subtended by the entrance pupil of the detector to the screen (Ωdet) is dependent on the aperture size. In case the detector solid-angle is smaller than the solid-angle subtended by the exit pupil of the projection system to the screen (Ωproj), the projection optics are capable of illuminating any of the N = Ωproj/Ωdet uncorrelated sub-resolution areas within a single detector resolution spot on the screen. The speckle contrast can in this case be reduced by a factor . This is only possible with projection systems where the coherence of the laser beam is sufficiently reduced such that spatial decorrelation occurs on the projection screen.
2.3. F-number of the camera lens
The average size of a speckle spot can be described as the equivalent area of the normalized covariance function of the speckle intensity , which we will call the coherence area Ac. It is determined by the ratio of the focal length and the clear aperture of the camera lens, i.e. it is dependent on the f-number of the camera lens. The average size of the speckles is given by Eq. (2) can be written as Eq. (3) defines the average size of the speckles that can be created in a lens-produced image.
As a consequence, the f-number of the camera has an influence on the measured speckle contrast because it determines the average size of the speckles in relation to the area of the camera pixels. When the average speckle size is similar or smaller than the pixel area, spatial integration of the speckle occurs, an effect known as spatial averaging. In , it was derived that the reduction in speckle contrast is given by the square root of the ratio between the pixel and speckle size , where Ap is the area of the camera pixel.
In Fig. 2(b), we plot the speckle contrast measured with the setup of Fig. 1, where we change the f-number by varying the diameter of the aperture stop of our camera lens, thereby also varying the clear aperture. The marked points are measured values and the line is the interpolation. In , it was deduced that in the case of unsuppressed speckle (with a static diffuser) the speckle pattern consists of a superposition of a coarse and fine speckle. A rotating diffuser avoids the coarse speckle and changes the interference condition on the screen. As such, the speckle generated at the screen is altered. This results in a reduction of the speckle contrast. We can observe in Fig. 2(b) that in case of unsuppressed speckle, the speckle contrast increases and saturates for increasing f-number of the camera lens. In the case of suppressed speckle, the speckle contrast first increases and then decreases.
In Fig. 2(a), a simulation of the speckle contrast as a function of is depicted. This result is obtained by simulating a fully developed speckle pattern with exponential statistics, as was described by Duncan and Kirkpatrick . The marked points result from the simulation, the line shows the interpolation. The pixel area is steadily increased and the averaging effect results in a reduction of the speckle contrast. One can see that the linear behavior of the speckle contrast in function of is only valid in a narrow region. For large speckle sizes (with Ap small), no spatial averaging occurs and the speckle contrast remains unaltered. The unsuppressed speckle measurements correspond well with the previously described simulation model.
The situation increases in complexity once the diffuser starts rotating, thus providing a coherence reduction of the laser illumination. Therefore, the suppressed speckle is influenced by two different effects. For small f-numbers, the spatial averaging effect is clearly visible. At larger f-numbers, there is a clear decrease of the speckle contrast. This can be understood if one takes into account that the ratio Ωproj/Ωdet is becoming larger than one and the speckle contrast is reduced as a result of spatial decorrelation of the projected light due to the rotating diffuser (see Section 2.2).
2.4. Distance of the camera
If we change the distance (d) between the camera lens and the screen, we only change the solid-angle subtended by the entrance pupil of the detector to the screen (Ωdet) (we can neglect the effect of refocusing on the numerical aperture of the imaging system if the camera is at a sufficient distance from the projection screen). In our experimental set-up, the camera was varied in distance from 1 to 2.5 m, which is equivalent to a distance/screen height ratio of 1.14 to 2.19. The result is depicted in Fig. 3, where we observe a linear relationship between the reciprocal of the distance and the speckle contrast. This is in agreement with the theory which says that the speckle contrast decreases by a factor , where D is the clear aperture of the detector and d is the distance between camera and projection screen.
2.5. Integration time of the image sensor
The integration time of the image sensor can also influence the speckle contrast measurement. Consider the case of a vibrating screen as a speckle reduction technique, illustrated in Fig. 4. Since the imaging system is diffraction limited, the screen is sampled with a finite imaging resolution spot. If the screen is translated, different secondary wavefronts will emerge from within the resolution spot, possibly resulting in a different intensity value at the corresponding detector pixel(s). In case this movement occurs within the integration time of the image sensor, the speckle contrast can be reduced. In order for the speckle contrast to be reduced with a factor , the screen has to move over a distance equal to N observer resolution elements and this within the integration time of the image sensor. Analogously, the minimal speed of a rotating diffuser to suppress speckle can be understood. In the experiments, we noticed that even for slow angular rotations (<5 Hz), the speckle contrast is maximally reduced. One has to remark that in case of a vibrating screen at large distance from the viewers, the design challenges are more crucial. Ideally, the screen should be translated over large distances, but in reality, this translation will be restricted.
The experimental results presented in the previous sections could lead to the (false) assumption that the measured speckle contrast values corresponding to different measurement configurations are connected by specific equations. This might be true for fully optimized projection configurations of which we know exactly which speckle reduction method(s) are used. For practical projection displays that use different, although not necessary fully optimized, methods this will certainly not always hold. In order to illustrate this in detail, we again consider our experimental configuration (see Fig. 1). In the following, we examine the speckle contrast as a function of the camera lens’ f-number at two different positions. We noticed that the behaviour is different depending on the distance of the measurement setup. This is depicted in Fig. 5. One can see for example that for the speckle contrast measured at 700 mm, the speckle contrast is continuously rising for increasing f-number. At a distance of 470 mm, the speckle contrast appears to be levelling and the effect of varying the f-number on the speckle contrast is limited. As a consequence, in case the speckle contrast was measured at a certain f-number, it is almost impossible to know the speckle contrast at another f-number. Therefore, it is essential to measure the speckle contrast in a consistent manner such that the speckle contrast can be precisely and reproducibly determined. This means that the relevant parameters of the measurement set-up should be fixed.
3. Standardized speckle measurement procedure matched to human perception
Our goal is to define a speckle contrast measurement procedure which is in correspondence with the subjective speckle perception of a human observer. This value should be independent of the laser projector illumination configuration and of the used speckle reduction method(s). The best way to guarantee this is to choose a measurement configuration that is in correspondence with the human imaging system, i.e. the eye. This does not imply that we intend to mimic the human eye, which is an almost impossible task and has previously been investigated , but rather choose appropriate values for the relevant parameters of our speckle contrast measurement configuration.
3.1. Characteristics of the human eye
Vision is a fundamental aspect of our primary senses and one of great complexity. Essentially, all parts of the eye are important in perceiving a good image. Different parameters influence the image quality, one of which is the pupil size. Large pupils reduce diffraction but the eye resolution is also limited for large pupil sizes by the aberrations of the eye lens . The pupil size is largely dependent on the luminance of the projected image . As a test case, we consider an indoor theater situation where the luminance is fixed according to the industry standard for indoor motion-picture film (48 cd/m2) . Different illumination levels perturb either the rod (scotopic) function or the cone (photopic) function of the retina. The luminance used in theaters corresponds with a situation where photopic vision is dominant. In , an estimation formula for the pupil diameter based on the luminance is given. In this situation, a pupil diameter of 3.2 mm is obtained. In , it is shown that in case the height variance of a rough surface is very large, optical aberration effects on speckle are asymptotically ignorable. Since this is on average the case for a typical cinema screen, the average speckle size is only defined by the diffraction effects of the pupil diameter. Using Eq. (3) with a pupil diameter of 3.2 mm and an image focal length of the human eye of 22.8 mm , the average speckle size is approximately 18.29μ m2.
Another vital element that influences human visual perception is the retina. Important in the context of speckle measurements is to determine the ratio between the human pixel size and the speckle size, i.e. the ratio from Section 2.3. The density of the cones at the fovea, responsible for photopic vision, vary in position with a maximum at the fovea centralis . Since the fovea provides the sharpest resolution, the eyeball is continuously moving such that the light from the object of primary interest falls on this region. Based on the work of Curcio , one knows that the average cone density at the fovea is approximately 191000 cones per mm2. Therefore, the average human pixel size is 5.24μ m2. The square root of the ratio between the human retinal mosaic pixel area and the speckle size in a cinema environment is then equal to . It should not be surprising that the retina sampling satisfies the Nyquist criterion and as such guarantees optimal imaging for a human observer.
3.2. Speckle contrast measurement setup
The measurement system consists of a camera lens and a digital image sensor. We match the relevant parameters to the human visual system, i.e. a clear aperture of 3.2 mm and an (see Section 3.1). Remark that we always assume a diffraction limited camera lens. In that case, the ratio of the pixel to speckle area ( ) defines the necessary f-number of the camera lens. Using Eq. (3), we find thatTable 1, an overview is provided (based on Eqs. (4) and (5)) of the necessary f-number and focal length of the camera lens for a given pixel area. For this table, the wavelength is set to 532 nm, the clear aperture to 3.2 mm and to 0.54. We assume that the pixels of the detector have a square footprint.
Furthermore, it is important that the dynamic range of the camera allows for accurate measuring without the influence of discretization errors. It is our experience that a minimal bit-depth of 6-bit is adequate to sample the speckle pattern. Internal wavelength filters in the camera can exert an influence when the cut-off wavelength of these filters is in proximity of the primary colors of the projection system. One has to ensure that the cut-off wavelength of the filter(s) is outside the incoming light spectrum of the primary sources.
If we aim for a fair speckle quality measurement, the speckle contrast has to be measured in the viewing condition that provides the highest value. Depending on the used speckle reduction mechanism(s), this can vary. Consequently, the distance at which the highest speckle contrast is measured, should be mentioned.
If any movement occurs within the integration time of the camera, the speckle image on the image sensor will change, which can lead to an incorrect speckle contrast value.
Incorrect focusing of the camera lens on the screen can result in large deviations of the measured speckle contrast value. This effect was measured using the projection setup as depicted in Fig. 1 and the CCD camera was positioned at a distance of 2 m from the projection screen. The focus of the lens was varied from 1.2 to 7 m. In Fig. 6, we plot the measured speckle contrast as a function of the focus distance of the camera lens. The marked points are the measurements and the line is a fit. In case the lens is not in focus, the amount of speckle is much lower than when the lens is in focus. As a human observer looking at an image on the screen will focus his/her eye on the screen, placing the lens out focus results in a speckle contrast measurement that is not linked to human perception of the amount of speckle. As a consequence, it is essential to focus the camera lens onto the screen surface.
Ambient lighting can seriously reduce the measured speckle contrast so maximum reduction of the (background) illumination is required. The level of ambient lighting must be smaller than the least significant bit of the dynamic range. The integration time of the detector is set to 50 ms, corresponding with the temporal integration time of the human eye . For projection systems without a specified projection screen, a standard projection screen should be determined to perform the speckle measurements.
3.3. Post-processing of the speckle contrast
We propose the speckle contrast to be measured separately for the (three) primary, uncorrected colors of the projection display. This is necessary because different speckle reduction phenomena can be active for the different primary colors of the projection system.
First, we capture the speckle pattern on the CCD. The area of this image (Aimage) has to be large compared to the speckle size (Ac) in order to correctly measure and calculate the speckle contrast. In Fig. 7, the speckle contrast is plotted as a function of the ratio of the image area to the average speckle size. In these measurements, the area of the image is increased and the corresponding speckle contrast value is calculated. As the results illustrate, the standard deviation of the speckle contrast calculation decreases for increasing image area and the speckle contrast value converges. Therefore, a ratio Aimage/Ac of at least 1 × 104 should be used.
Possible background intensity fluctuations can occur due to for example screen nonuniformities. We have noticed that the latter results in an overestimation of the speckle contrast. The spatial frequency of the background intensity fluctuations is small compared to the speckle. Thus, their effect can be removed by using a high-pass filter. We first subject the image to a low-pass mean spatial filter. The originally measured intensity distribution is then divided by the filtered one. This results in a new distribution from which slow variations of the intensity are removed.
The low-pass spatial filtering is performed by calculating the spatial convolution between the image and a kernel. We used a normalized circular kernel with radius Npixels. Such a filter smooths the image by replacing each pixel intensity by the neighbourhood mean intensity. The area of the kernel Akernel = π(Npixels)2 × Ap, with Ap the pixel size, determines the spatial cut-off frequency of the filter. The influence of the kernel area on the calculated speckle contrast is depicted in Fig. 8(a), where the speckle contrast is plotted as a function of . These values are obtained by increasing the kernel area of the filter for a typical speckle pattern.
If the area of the filter’s kernel is small compared to the average speckle size, the resulting speckle contrast value does not correspond with the perception of the speckle. This is because the background intensity, calculated with this filter, contains a large amount of the speckle pattern. This is depicted on the top left of Fig. 8(b). As a result, also part of the speckle will be filtered out. The larger the kernel area, the more we merely obtain background intensity fluctuations in the low-pass filtered image. We also need to keep in mind not to increase the kernel size too much because otherwise some of the background intensity variations will still be present in the final image. This leads to an unwanted increase in the image intensity’s standard deviation and thus results in an overestimation of the speckle contrast. As a rule of thumb, we have noticed that the value should approximately be between 3.5 and 5.
4. Subjective speckle perception tests
Now we would like to apply the developed measurement configuration to a laser projection system of which we can vary the level of speckle. In addition, a test group will evaluate different speckle contrast levels.
The subjective speckle measurements were performed making use of a laser projection system in which it is possible to vary the speckle contrast in a gradual manner by changing certain internal projector settings. Additionally, light of a white lamp projector was added to some patterns in order to further reduce the perceived speckle contrast. A test group of 40 people (technically and non-technically oriented) with 20/20 vision were subjected to a speckle perception test. The test people were asked to verify for every color bar whether or not speckle was still visible. The test pattern consisted of three horizontal saturated color bars, namely red, green and blue (see Fig. 9(a)). The image was visualized for 10 seconds and then 15 seconds were given to answer the question. The luminance of the projected images was set to 30 cd/m2. During the subjective speckle perception test, we first showed these color bars with the highest speckle contrast values and then we gradually decrease the amount of speckle to the point of which we assumed that speckle should no longer be visible for the human eye. Afterwards, the entire sequence is cycled through in reverse order. The test group was positioned at a distance of 2.3 times the screen height (see Fig. 9(b)).
The results of the subjective measurements can be seen in Fig. 10. It is important to point out that the following measurements were performed as an evaluation for the proposed speckle contrast measurement. It is not our intention to draw any strong conclusions related to the subjective speckle perception threshold. The latter will be investigated for a larger test group and described in future work.
As mentioned previously, the speckle contrast was first lowered and afterwards again raised in the same number of steps. Therefore, CR1 corresponds with the color bars with the highest speckle contrast, CR6 with the lowest speckle contrast value. In Fig. 10, the percentage of the people that confirmed that speckle is present is plotted for the different colors and speckle contrast values. One can observe that in the case of red light, for the large majority of people, CR6, CR5 and CR4 are not noticeable. CR3 is perceived by approximately half of the test group, CR2 and CR1 by a slightly larger amount. In the case of green light, CR6 and CR5 are perceived by approximately 20% of the test group, CR4 appears to be more perceived when preceded by images with a larger speckle contrast value. CR3, CR2 and CR1 are detectable by almost everyone. In the case of blue light, for all speckle settings, the large majority of the people never saw speckle in this color bar.
These speckle contrast values were measured using the previously mentioned speckle contrast procedure. The results can be found in Table 2. The speckle contrast was calculated at a distance of one screen height, with a CCD detector with a pixel size of 4.40 × 4.40 m2 and a camera lens with an f-number of 16 and a focal length of 52 mm.
The speckle contrast corresponding with for example CR1 is different for all colors investigated. In order to obtain an overview of the subjective perception for every color, a histogram of the subjective speckle perception is provided (see Fig. 11). The graphs represent the percentage of the people that confirmed speckle was present for different speckle values, and for the different investigated colors. The axes on the histograms are equal. The first descending part of the x-axis represents the first part of the test sequence, i.e. CR1 to CR6, the second ascending part of the x-axis represents the remaining part of the sequence, namely CR6 to CR1. The empty bins in Fig. 11 correspond with the speckle contrast values that were not evaluated.
As part of the future work, the derived speckle measurement procedure will be exerted to determine the subjective speckle contrast threshold for a larger test public.
The important parameters when measuring speckle of projection systems are analyzed and illustrated for different projection set-ups. We are able to provide certain values for these parameters such that the measured speckle contrast is a good merit function for the subjective perception of the speckle phenomena by humans. A specific measurement configuration and methodology to derive consistent speckle contrast values is proposed. This measurement set-up and methodology was used to obtain the different speckle contrast values of different laser projected images that were used in subjective speckle perception tests of a group of 40 people. We believe that this measurement method could be used as a possible blueprint for a standardized speckle measurement procedure.
The authors would like to thank Barco n.v. for the valuable discussions and for providing the indispensable laser projector prototype. Stijn Roelandt’s and Gordon Craggs’ research are funded by the Agency for Innovation by Science and Technology in Flanders (IWT). The authors would furthermore like to acknowledge financial support from the Agency for Innovation by Science and Technology in Flanders (IWT), the Industrial Research Funding (IOF), Methusalem VUB-GOA, the Interuniversity Attraction Pole programme “Photonics@be”, and the OZR of the Vrije Universiteit Brussel.
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