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A Simple Imaging-Based Technique for Quantifying Haze and Transmittance of Materials.

INTRODUCTION

Haze and transmittance are important optical properties of materials such as commodity plastics [1-5], particularly in packaging applications [6], where low haze and high transmittance allow the consumer to clearly see the product at point-of-sale. For these materials, a widely used method for quantifying both properties is described in the industrial standard ASTM D1003 Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics [7], The standard defines haze as the percentage of the total light transmitted through the sample which is scattered by >2.5[degrees] from the direction of the incident beam, while luminous transmittance is defined as the ratio of light transmitted through the sample and the incident light.

To expand on these definitions, haze quantifies the turbid, cloudy appearance of, for instance, semicrystalline polymer films which arises from light-scattering and reflection/refraction due to refractive index inhomogeneities on visible light wavelength scale (400-700 nm) [1, 8, 9]. These inhomogeneities may be present in the bulk of the material--typically in the form of crystallites, voids, and additives such as pigments--as well as on its surface due to roughness and fabrication-induced imperfections [8], Consequently, an increase in the value of haze corresponds to a reduction in the contrast of objects viewed through a material sample. In this context, "contrast" refers to the local difference in the light intensity (bright vs. dark) detected for the small, barely-resolved features of objects; contrast reduction thus implies loss of image detail [10], Transmittance quantifies the extent to which light intensity is attenuated after passing through a sample. As in the ASTM D1003 standard [7], we shall specifically refer to diffuse transmittance throughout the manuscript, which integrates the transmitted light intensity over a large range of angles. This implies that a reduction in transmittance is related mainly to absorption and reflection losses, rather than the off-axis deflection of transmitted light due to scattering.

In the state of the art, haze and transmittance are most commonly measured using a dedicated haze meter instrument, consisting essentially of a calibrated light source and an integrating sphere to collect the light transmitted through the sample [11]. While commercial haze meters are readily available and easy to operate, their use incurs several disadvantages. The first of these is the arbitrary quantitative definition of haze by the ASTM D1003 standard [7], since the angular specification of 2.5[degrees] for the minimum deviation of incident light appears to be entirely indiscriminate [12], Hence, such definition does not directly correlate with the more practical description of haze based on the loss of object contrast incurred by viewing it through a turbid material sample. Second, a typical haze meter requires large (~5 [cm.sup.2] area) and maximally homogeneous material samples for obtaining meaningful results since the measurement output is a single value averaged over the entire illuminated area. Third, the moderately high price tag of the commercial haze meters, as well as the limited optical data they provide, makes their use impractical for conducting exploratory research on laboratory scale when more sophisticated, local data on the optical properties may be needed, thereby presenting an obstacle for further development of novel materials and clarifying additives.

Here we present a simple and versatile technique that uses virtually ubiquitous hardware and provides spatially resolved information on both haze and transmittance, while also being substantially more efficient in terms of material use compared to alternative methods. The method is based on photographic imaging of at least partially transparent samples placed in direct contact with--and backlit through--a "knife-edge" array mask. Since it is an imaging-based technique, haze is unambiguously defined in the practically-useful terms as the reduction of perceived image quality of the objects viewed through a material sample. Moreover, the extracted haze values specifically correspond to the overall contact haze, compared with simply the "overall" haze in the case of conventional haze meters. The presented imaging-based technique is therefore expected to be more suitable for the characterization of, for instance, commodity plastics for packaging applications. Additional applications could involve the evaluation of optical properties, as well as the spatial homogeneity thereof, for dispersions, coatings and films.

As a specific example, we analyze haze and transmittance for a series of injection-molded disk-shaped plaques of a semicrystalline polyethylene (PE) containing varied fractions of a commercial clarifying agent, designed to reduce the polymer's haze by optimizing its nucleation and crystallization behavior [2, 3, 13-15]. Furthermore, haze is also measured for commercially available ASTM D1003 haze standards and the results are compared with nominal values.

EXPERIMENTAL

Materials and Processing

Linear-low-density polyethylene (LLDPE) resin (DOWLEX[TM] 2552E; The Dow Chemical Company) and the clarifying agent l,2,3-trideoxy-4,6:5,7-bis-O-[(4-propylphenyl)-methylene]nonitol (TBPMN, Millad[R] NX[TM] 8000, Milliken Chemical) were used as received. PE/additive blends comprising 0.25% and 2% w/w TBPMN were compounded for 5 min in a laboratory co-rotating mini-twin-screw extruder (Xplore[R] MC 15, 15 mL total volume, Xplore Instruments BV, The Netherlands) operated at 220[degrees]C and 40 rpm under a nitrogen blanket. The molten blends were extruded directly into a laboratory micro injection molder (Xplore[R] IM 12, 12 mL total volume, Xplore Instruments BV, The Netherlands) and injected into a mold kept at room temperature to yield circular plaque samples (1 mm thickness, 26.6 mm diameter). A reference sample of the neat polymer was produced using the identical procedure.

Instrumentation and Imaging

Figure la shows a schematic illustration, as well as the actual set-up, of the imaging-based technique reported herein. The polymer plaque samples were placed onto a laser-cut stainless steel mask (0.1 mm thickness) and illuminated from below using a light-emitting diode (LED) (Cree XM-L T6 Cool White) operated at constant current (1.5 A; equivalent to ~3.6 V and ~5 W). Prior to being incident on the masked samples, the light beam from the LED was passed through a 1.5-mm thick polytetrafluoroethylene (PTFE) sheet acting as a light-diffuser, thus producing spatially homogeneous illumination. The majority of the area around the sample was obscured with a metal ring which also ensured a firm contact between the sample and the mask. The samples were then photographed from the upper side using a digital camera (Canon EOS 6D DSLR, 5,472 X 3,648 pixels, Canon Inc., Japan). The entire assembly was placed on a single optical axis and, for improved accuracy, integrated within a customized optical microscope stand (MS5, Leica Microsystems GmbH, Germany) as shown in Fig. la. All photography was carried out in a dark room.

The mask consisted of a simple grid pattern comprising 2 mm wide stripes separated by 2 mm wide gaps, resulting in a sequence of alternatingly masked (dark) and backlit (bright) areas on the sample.

Custom white balance of the camera was performed prior to placement of the mask and the sample. (This step simplifies the experimental method compared to that using a spectrophotometer since, in the latter case, the reflectance of the integrating sphere and the light-trap shutter need to be carefully matched [12]). Color photographs of the polymer plaque samples illuminated through the mask were taken with a macro lens (50 mm f/ 2.5, diagonal angle of view = 46[degrees]) fixed at a constant distance from the sample (image scaling = 76 pixels per mm [px/mm] mask size). The camera was focused onto the mask without a sample using its built-in autofocus feature (phase detection mode); focus was then locked for the subsequent sample images. Other adopted camera settings included a fixed aperture (f/10): sufficiently small in order to ensure a depth of field larger than the sample thickness, but not exceedingly small to avoid diffraction effects. Shutter time was set by the camera's built-in autoexposure feature. A low sensitivity (ISO 200) was used for reduced noise. Photographs were saved in raw (Canon CR2) format, thereby avoiding any potentially distorting image processing steps inherent to the jpeg-compression algorithms.

For reference, the transmittance and overall haze of the injection-molded plaque samples were also determined using a conventional haze meter (Haze-Gard Plus, equipped with CIE Standard Illuminant C, BYK-Gardner GmbH, Germany) conforming to the ASTM D1003 standard [7]. Transmittance of these samples was additionally measured using a UV-Vis spectrophotometer (UV-2600, Shimadzu Corp., Japan) equipped with a diffuse reflectivity (integrating sphere) attachment. The recorded spectra were not corrected for reflection losses since reflectance was likewise not accounted for in the haze-meter-based transmittance measurements. The resulting transmittance values for the polymer plaque samples are given in Table I for incident light wavelength = 510 nm, corresponding to the typical wavelength of a digital camera's maximum spectral RGB sensitivity [16]. Full transmittance spectra are shown in Supporting Information Fig. Sia.

Image Analysis

The analysis of the digital photographic images involved, in essence, quantifying the spatial distribution of light intensity detected for the backlit and unlit areas of the samples, as well as the sharpness of the transitions between them. First, using the Adobe Photoshop CS6 software with Camera Raw 9.1.1 plugin, the CR2 photographic files were opened as color images ("Adobe RGB 1998" profile assigned) and converted to 8-bit grayscale images (default settings, "Gray Gamma 1.8" profile assigned). The gray value, G, range of each image was normalized by selecting as black (G = 0) and white (G = 255) points, respectively, the stripe of the mask in an area not covered by the sample and a backlit area on the sample, as shown in Fig. lb. The images were subsequently saved in the uncompressed TIFF format and are presented in Fig. 2 (top row). Second, quantitative analysis of the TIFF image files was performed using the ImageJ software [17].

Haze. The calculation of haze requires the image's modulation transfer function (MTF) to be determined, with MTF quantifying the contrast between dark and bright image regions as a function of spatial frequency [18]. (The reader is directed to Note 1 in the Supporting Information for a detailed description of the calculation and application of MTF in image analysis.) To this end, a 150 X 150 pixel square selection of a vertical dark-tobright transition was made such that the dark, masked side is on the left and the bright, backlit side is on the right (see Fig. lb). Such a selection allows for straightforward "one-click" calculation of the MTF using the ImageJ SE_MTF_2xNyquist.jar plugin [19]. The adopted plugin options were: line pairs per mm (lp/mm) for "Frequency units," 18 mm for "Sensor size," 1,372 for "Number of photodetectors" (76 px/mm mask size), and 128 pixels for "Sample size" [20].

The resulting MTF curves for the imaged polymer plaque samples are shown in Fig. 2 (fourth row). In order to obtain the corresponding haze reference, MTF was also determined for the illuminated mask in the absence of the sample, which was taken as the 0% haze standard. The sample's haze spectrum as a function of spatial frequency / is calculated using Eq. I, and the final haze value is then determined from the average of the haze spectrum within a chosen spatial frequency range (5-10 lp/mm) using Eq. 2:

Haze spectrum (f) = 1 - MTF[(f).sub.sample]/MTF[(f).sub.reference] (1)

[mathematical expression not reproducible] (2)

where [f.sub.1] and [f.sub.2] represent, respectively, the lower and upper limits of the chosen spatial frequency range.

Transmittance. For quantifying transmittance, a rectangular selection was made inside a backlit (that is, not covered by the mask) area of the imaged sample near its center. The selection's average gray value was used for the calculations, with higher values corresponding to higher transmittance. To provide a reference for the transmittance measurements, the corresponding data was also recorded for the illuminated mask in the absence of the sample, hereafter simply referred to as the "reference," which was taken as the 100% transmittance standard. Hence, the transmittance value for a given sample was calculated using Eq. 3, with (G) representing the average gray value for the selected backlit area:

Transmittance (%) = [<G>backlit sample/(G)backut reference] x 100 (3)

We emphasize that, despite its seeming complexity, the image analysis described above can be straightforwardly performed using widely-available software such as ImageJ [17, 21].

RESULTS AND DISCUSSION

Figure 2 (top row) shows the gray scale photographs of the backlit mask ("reference") and the three polyethylene (PE) samples, the transmittance and haze of which vary depending on the relative content of the TBPMN clarifying agent. The first visual impression is that of different transmittance among the samples, with sample (c) (PE/2% TBPMN) featuring the lowest transmittance as evidenced by the lowest brightness (i.e., gray value) for the backlit/unmasked areas of the sample. The close-up views shown in the second row of Fig. 2 highlight further differences between the samples in terms of the relative sharpness of the object imaged through them (i.e., the dark-to-bright transitions for the mask). The sharpness appears to be diminishing from left to right, with reference a) expectedly featuring the sharpest transitions and sample (d) (neat PE) the most blurred. The same trend of decreasing dark-to-bright transition sharpness can be inferred from the increasingly rounded and less sloping sigmoidal shape of the transitions' gray value profiles (cf. edge spread functions (ESF) in Fig. 2, third row).

Haze

In order to determine haze, modulation transfer functions (MTF) were calculated for the dark-to-bright transitions in the reference and sample images shown in Fig. 2. The resulting MTF curves, presented in the fourth row of Fig. 2, show several salient features. First, all MTF curves reach zero value at spatial frequencies f [less than or equal to] 30 lp/mm--that is, substantially below the calculated Nyquist frequency (38 lp/mm)--indicating that the photographic resolution is adequate for the presented analysis [22, 23]. Second, it can be seen that the MTFs for the reference (a) as well as samples (b) and (c) reach zero at f [approximately equal to] 25-30 lp/mm, while the corresponding value for sample (d) is ~10 lp/mm. The spatial frequency value at which MTF = 0 indicates the smallest distance between two radiating points at which they can still be distinguished. As such, this provides a relative measure for the reduction in resolution of the mask image incurred by placing a material sample on top of it, signifying, as can be expected, that sample (d) (neat, unclarified PE) allows for the lowest optical resolution. Third, all MTF curves exhibit a distinct shape, characterized by a virtually linear section at intermediate frequencies, bounded by nonlinear tail-in and tail-off sections at low and high frequencies. The presence of these linear MTF sections over a given frequency range yields plateaulike sections in the resulting haze spectra calculated using Eq. 1 (see Fig. 2, bottom row) which, in turn, provides a robust method for calculating haze.

Figure 3a shows the MTF curves obtained for the reference and sample images presented in Fig. 2 replotted on a common scale, with the corresponding haze spectra calculated using Eq. 1 given in Fig. 3b. At spatial frequencies f < 5 lp/mm, the values of haze spectra approach zero by virtue of MTF normalization, while at f > 10 lp/mm the corresponding values show strong fluctuations due to the corresponding MTFs approaching zero. Hence, the 5-10 lp/mm spatial frequency range (cf. shaded regions in Fig. 3a and b) was deemed to offer the best compromise between the above-mentioned factors, while also exhibiting essentially constant, frequency-independent haze spectrum values. We note that this spatial frequency range closely matches the typical resolution of the human eye at 20 cm viewing distance (~6 1p/mm) [24], which further emphasizes the relevance of the chosen 5 to 10 lp/mm frequency range for characterizing the optical properties of materials envisaged for packaging applications.

Consequently, single haze values for the individual polymer samples were determined according to Eq. 2 using the average values of the haze spectra in the 5 to 10 lp/mm spatial frequency range. Since a haze meter measures optical properties over a comparatively large (typically ~5 [cm.sup.2]) sample area, haze values via the photographic method were determined at five points on each sample as indicated in the inset of Fig. 3c. The resulting haze values are presented in Fig. 3c alongside the corresponding values obtained using a haze meter. Excellent qualitative agreement is found for the haze values determined using the two different techniques, with haze increasing in the sample order (b) < (c) < (d), with the neat, unclarified PE sample (d) expectedly featuring the highest haze.

Finally, the presented method for determining haze was further tested on commercially available ASTM D1003 haze standards comprising injection-molded poly(methyl methacrylate) (PMMA) containing varied fractions of colloidal silica-based additives. The results are presented in Supporting Information Fig. S3 and Table SI, and are found to be fully consistent, showing the same key features: namely, plateau in the haze spectra for the 5 to 10 lp/mm spatial frequency range and complete qualitative, as well as excellent quantitative (with an average difference in values of only 1%), agreement with the nominal haze values. This confirms the general applicability of the presented photographic method irrespective of the specific polymeric materials and, more importantly, the exact nature of the scattering centers.

Transmittance

Transmittance of the samples was calculated by means of Eq. 3, taking the average gray value for the backlit/unmasked areas near the center and treating the corresponding value for the mask itself as the 100% standard. The results are presented in Table 1, where they are also compared with the corresponding values obtained using a conventional haze meter and UV-Vis spectrophotometer--the latter equipped with an integrating sphere to specifically record diffuse transmittance. It was found that transmittance is marginally reduced with increasing content of the clarifying agent, with neat PE (cf. Fig. 2d) exhibiting the highest transmittance (93%) and PE/2% TBMPN (cf. Fig. 2c) the lowest (88%). As such, transmittance determined using the presented photographic method shows excellent qualitative agreement with the corresponding data obtained using the two alternative techniques. The origin of the differences in the absolute transmittance values will be further discussed below.

DISCUSSION

Comparison with Other Haze and Transmittance Analysis Techniques

Figure 3c and Table 1 confirm the excellent qualitative agreement for haze and transmittance values obtained by the presented photographic method and the measurements performed using a conventional haze meter. Both methods provide similar haze and transmittance rankings for the three tested samples. However, differences are evident in the quantitative data; notably, the photographic method yields marginally lower haze values and higher transmittance values compared with those recorded using a haze meter.

The reasons for the observed discrepancy in the measured haze values are rather complex, with the most important contributing factor expected to be the different definition of haze in the two methods. While the ASTM D1003 standard [7] defines haze as the percentage of the total light transmitted through the sample which is scattered from the direction of the incident beam by more than (arbitrarily chosen) 2.5[degrees], the presented imaging-based technique quantifies haze on the basis of a reduction in the perceived image quality. Thus, in general the two methods cannot be expected to be fully comparable. The reader is directed to Note 2 in the Supporting Information for further details.

The minor (10%--14%) discrepancy in transmittance values can be plausibly attributed to the differences in hardware. Specifically, the spectral response can be expected to vary for different illuminant/detector combinations. To confirm this, transmittance spectra of the samples were recorded using a UV-Vis spectrophotometer. Transmittance values at 510 nm, corresponding to the typical wavelength of a digital camera's maximum spectral RGB sensitivity [16], are given in Table 1 and, while showing qualitative agreement, are found to be lower than the values obtained both using the photographic method and the haze meter by ~24% and 12% respectively. Note that the three methods measure diffuse (rather than specular) transmittance, albeit with a smaller range of collecting angles for the photographic method compared with the haze meter and the UV-Vis spectrophotometer, on the basis of which the former may be expected to yield lower transmittance values. Since the opposite is observed, we infer that calibration issues are likely to be the primary factor responsible for apparent overestimation of transmittance values determined via the photographic method. This may be corrected by adjusting the image processing scheme, particularly during color-to-gray scale conversion, and with proper hardware profiling/calibration using transmittance standards. However, such adjustments were beyond the scope of the present work.

Modifications

The performance of the demonstrated technique can be straightforwardly enhanced and standardized in terms of, for instance:

i. Light source (mono- or polychromatic; collimated or uncollimated);

ii. Mask pattern (size and geometry of mask stripes/gaps);

iii. Image resolution (minimum required for obtaining valid MTFs).

Polarizers inserted above and below a masked sample could enable further information to be extracted from the photographic images taken in cross-polarized geometry, since the imaging system then functions as a simple polariscope. Our preliminary results shown in Figure 4 illustrate that such images could be used as an effective means for visualizing material flow and anisotropic crystallization under nonquiescent conditions for, among others, injection-molded polymer samples such as those analyzed above. It is immediately obvious that samples (b) and (c) (i.e. those containing the clarifying agent) exhibit spatially-inhomogeneous microstructure. Such inhomogeneities obviously affect the resulting local material haze. The reader is directed to Note 3 in the Supporting Information for a discussion on the possible origins of microstructure heterogeneity for the above-described samples.

As a further extension of the presented imaging-based technique, using more complex, two-dimensional grid masks could permit haze and transmittance to be spatially mapped, for instance in the so-called "diffusion-screening" experiments [5], which would allow for a rapid determination of the minimum haze value that can be obtained for a given polymer/clarifying agent combination. The additional use of polarizers would allow the local optical properties to be correlated with material flow during injection molding and the resulting spatiallyinhomogeneous crystallization.

CONCLUSIONS

A simple photographic imaging technique is presented for quantifying haze and transmittance of materials, requiring only inexpensive hardware and minimal material quantities. The method involves taking digital photographs of the material samples backlit through a "knife-edge" array mask and subsequently analyzing the 8-bit gray scale images. Haze is determined from the modulation transfer functions (MTF) corresponding to the gray value transitions between the masked (dark) and backlit (bright) regions, while transmittance is quantified from the absolute gray values recorded for the backlit/unmasked regions of the sample. Using a series of injection-molded polyethylene plaques as an example, the measured transmittance and haze values showed good agreement with those obtained using a conventional haze meter instrument conforming to the ASTM standard.

Notably, the presented imaging-based technique quantifies haze in a practically-useful way--based explicitly on the reduction of perceived image quality of the objects viewed through a turbid material sample--instead of the more empirical ASTM definition using an arbitrarily-chosen minimum scattering angle. Given that the mask is placed in direct contact with the material samples and, therefore, specifically the contact haze is quantified, the presented technique is expected to be particularly useful, for instance, for characterizing the optical properties of polymeric materials envisaged for packaging applications. Local optical properties can also be probed, while additional modifications can enable improved quantitative performance and extend the range of information that may be extracted.

A patent application (EP16191416.3) has been filed based on the technique reported herein. Subsequent studies will investigate the increase in haze as a function of the distance between the knife-edge mask and material samples, given that both "contact" and "out-of-contact" haze are highly relevant for commodity plastics industry, while also extending the range of analyzed material systems.

ACKNOWLEDGMENTS

Authors thank Prof. Paul Smith (ETH Zurich) for supporting this work, and for the many stimulating discussions and constructive suggestions. We further thank Werner Schmidheiny for his expert help in manufacturing essential experimental hardware. The Dow Chemical Company is acknowledged for supplying the polyethylene resin used in this study. Dr. Seda Aksel is thanked for providing the polymer plaque samples. Finally, Dr. Philipp Busato is gratefully acknowledged for unbiased discourse and for pointing out the authors' oversight of the proverbial needle in the ... hazetack.

REFERENCES

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[9.] A.J. Peacock, Handbook of Polyethylene: Structures, Properties and Applications, Marcel Dekker, New York (2000).

[10.] ISO International Standard ISO 12233 (Second edition). Photography - Electronic Still Picture Imaging--Resolution and Spatial Frequency Responses (2014).

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[19.] The plugin is geared to perform calculations on slanted edges (slanted in relation to the photographic sensor grid), but works just as well on vertical edges (at the expense of giving away the oversampling capability built into the slanted edge algorithm).

[20.] The values chosen for "Sensor size" and "Number of photodetectors" represent not the resolution of the camera's sensor (px/mm sensor size), but rather the resolution of the masked sample's photographic image (px/mm mask size; here 76 px/ mm). This results in spatial frequency values, expressed in line pairs per mm (lp/mm), that are independent of both the camera's exact sensor dimensions/pixel number (i.e. independent of the camera model) and the image scaling (i.e. independent of the camera lens' focal length and the distance sensor-to-sample). Thus, any changes in the sensor resolution or image scaling will merely change the Nyquist frequency (see [22,23]), but not the spatial frequency values.

[21.] For example, from the International Standards Organization (<www.iso.org>, ISO 12233 "Photography--Electronic still picture imaging--Resolution and spatial frequency responses"), from Imatest LLC (<www.imatest.com>) or from the National Institutes of Health (<imagej.nih.gov/ij>, Java-based public domain software ImageJ).

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[23.] In a discrete sampling system, such as a digital camera, there exists a sampling-rate-dependent upper signal frequency--the so-called Nyquist frequency--above which undersampling will fail to capture all the information from a sampled scan. In the spatial frequency domain of interest here, a minimum of two pixels are required to sample one line pair (comprising one dark and one bright section of a pattern), resulting in a Nyquist frequency of 38 lp/mm for the digital images analyzed in this work.

[24.] H. Weber, Digitale Farben in der Medienproduktion und Druckvorstufe, MITP Verlag, Heidelberg, Germany (2006).

Stephan Busato [iD], Aleksandr Perevedentsev

Department of Materials, Eidgenossische Technische Hochschule (ETH) Zurich, Vladimir-Prelog-Weg 5, Zurich 8093, Switzerland

Additional Supporting Information may be found in the online version of this article.

Correspondence to: S. Busato; e-mail: stephan.busato@alumni.ethz.ch

DOI 10.1002/pen.24580

Caption: FIG. 1. (a) Schematic illustration and an actual photo of the photographic imaging setup. The sample (depicted as a light-blue disk) is laid flat on the mask which, in turn, is placed onto a PTFE sheet (depicted as a gray disk) acting as a light-diffuser (A). A metal ring (B) is placed directly onto the sample to ensure its firm contact with the mask and to obscure any unwanted light around the sample. A light source (C) is used to illuminate the sample through the mask, and a photographic image of the sample is then acquired using a digital camera (D). (b) Schematic illustration of a typical photograph of the sample, showing the areas of the digitized image used for black- and white-point normalization as well as the square selection in the center of the image used for calculating the corresponding modulation transfer function (MTF). [Color figure can be viewed at wileyonlinelibrary.com!

Caption: FIG. 2. Digital grayscale photographs of the mask ("reference") and three polymer samples (polyethylene [PE] containing varied fractions of the TBPMN clarifying agent) placed onto it, with the corresponding image analysis details shown below. Top row: actual 2,000 x 2,000 pixel photographs; mask stripes and gaps are 2 mm wide, picture resolution = 76 px/mm. Second row: close-up views of the dark-to-bright transitions at the center of the images, highlighting the relative differences in gray values and transition sharpness. Third row: 8-bit gray value, G, profiles over the 128 px image width for the dark-to-bright transitions shown in the second row. Fourth row: modulation transfer functions (MTF) for the transitions shown in the second row; spatial frequency is expressed in line pairs per mm (lp/mm). Bottom row: haze spectra as a function of spatial frequency, calculated from the corresponding MTF curves (see text for details). Note that while only one dark-to-bright transition per sample is analyzed in rows 2-5, the use of a knife-edge array mask (as depicted in top row) allows such analysis to be performed at multiple locations on a sample.

Caption: FIG. 3. (a) MTF curves and (b) haze spectra for PE plaques containing 0.25% (dark gray lines and circles), 2% (gray lines and triangles), and 0% (light gray lines and rhombuses) of TBPMN clarifying agent (cf., respectively. (b)--(d) in Fig. 2). Data is shown for the central area of the samples (cf. Fig. lb). Also shown in (a) is the "reference" MTF (black line and squares) obtained for the illuminated mask in the absence of sample. The shaded regions correspond to the spatial frequency range (5-10 lp/mm) which was used for calculating the average haze using Eq. 3 and in which all MTF curves exhibit virtually linear behavior, (c) Comparison of average haze values obtained using the photographic method and a conventional haze meter (labeling as above). For the former, haze was recorded for five different spots on each sample, the positions of which are indicated by the red squares in the inset, with the corresponding error-bars highlighting the spatial inhomogeneity of haze. [Color figure can be viewed at wileyonlinelibrary.com]

Caption: FIG. 4. Color photographs (f/10, ISO 200) of the three injection-molded polymer samples taken in crosspolarized geometry, i.e., with orthogonal orientations of the transmission axes for the polarizers placed at the light source and the camera. The injection point is located at the bottom of the images. Note that the grid mask was not used for acquisition of these images. [Color figure can be viewed at wileyonlinelibrary.com]
TABLE 1. Comparison of the transmittance values obtained with a haze
meter, UV-Vis spectrophotometer, and the presented photographic
method.

Method         (b) PE/0.25%   (c) PE/2%   (d) PE
                  TBPMN         TBPMN

Photographic        92           88         93
Haze meter          81           74         83
UV-Vis (a)          69           60         72
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Author:Busato, Stephan; Perevedentsev, Aleksandr
Publication:Polymer Engineering and Science
Article Type:Report
Date:Mar 1, 2018
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