Evaluation of the spatial resolution of Gafchromic™ HD-V2 radiochromic film characterized by the modulation transfer function Open Access

Ion acceleration from laser-plasma interactions^1–3 is interesting for the development of hadron therapy,^4–6 proton radiography,^7–9 nuclear phenomena,¹⁰ and fast ignition inertial confinement fusion.¹¹ The ion beam specification for these applications typically requires high energy, high fluence, and monochromatic energy distribution. Much novel research is under way to improve beam performance. Laser-driven ions are characterized by extremely low transverse emittance and high peak beam current compared to conventional accelerator beams. These unique characteristics are expected for applications of laser-driven ions for FLASH¹² and PIXE¹³ analysis. The correlation between laser irradiation conditions and transverse emittance should be clarified to control the transverse emittance. In a typical transverse emittance diagnostic, the transverse momentum spread is determined from the spatial profile of the beamlet extracted by a slit or pinhole. In particular, laser-accelerated ions have a small spatial beamlet profile because the ion beam is generated by a small source of micrometer scale. A two-dimensional dosimeter with micrometer spatial resolution is necessary to diagnose small changes in this spatial profile. Two-dimensional profile measurements of laser-driven ions utilize a radiochromic film (RCF)^14–16 and a nuclear track detector (CR-39).¹⁷ Both detectors have advantages and disadvantages, but CR-39 has a low saturation dose and requires chemical etching with an alkaline solution, which compromises measurement convenience. On the other hand, no method has been established to evaluate the spatial resolution of the RCF as a dosimeter, taking into account the contrast. RCF will be useful as a dosimeter for emittance measurement if it can be shown to provide transverse profile diagnostics with micrometer spatial resolution similar to CR-39. For these reasons, we have decided to evaluate the substantial spatial resolution on the order of micrometers when RCF is used as a dosimeter in this paper.

In RCF, the active layer records the coloration, which is correlated with the dose of the ion beam, and the coloration is imaged by readout systems. As readout systems, microdensitometers were widely used until about the 2000s.^18,19 Since then, commercial base flatbed scanners, with the advent of high-end models, have been widely used for RCF dosimetry. These high-end models have a fast readout and a readout resolution of several micrometers in accordance with catalog specifications. Many studies have calibrated the correlation between Optical Density (OD) values and dose characteristics in RCF measurements with flatbed scanners.^20–24 OD represents the absorption rate of light of films. However, when RCF is used in combination with a flatbed scanner, artifacts caused by the characteristics of the light source and the monomer structure of the RCF are known to reduce measurement accuracy, and they have not been quantitatively evaluated.^25–28 Although these artifacts are known, very few studies have evaluated the spatial resolution and contrast of RCF measurements.^29,30 We will demonstrate the evaluating method for the spatial resolution characteristics of RCF dosimetry with a flatbed scanner using an MTF. A two-dimensional dosimetry system with high spatial measurement performance can image the OD distribution with high contrast at high frequencies. The MTF represents the relationship between spatial frequency and contrast and is the best index for evaluating the spatial resolution characteristics. Here, the RCF film Gafchromic HD-V2³¹ is used for evaluation because it has no protective layer on the front surface of the active layer and the film thickness is small. These characteristics of HD-V2 are expected to reduce the scattering of the transmitted light compared with other thicker RCFs. In the following, “RCF” is a reference to RCF in general, and “HD-V2” is a reference to the object of evaluation of RCF in this study. The flatbed color image scanner, Epson GT-X980, with 16-bit depth RGB, 6400 dpi reading resolution, and transmittance mode, is called “GT-X980.”

To evaluate the MTF of a readout system, a resolution test chart with a test pattern on a glass substrate is generally used. However, in this study, we need to evaluate the MTF of HD-V2 in combination with the flatbed scanner because the rod-shaped monomers of HD-V2 polarize or scatter the illuminating light and deteriorate the spatial resolution with the flatbed scanner. The square wave line patterns of a resolution test chart are transferred to the HD-V2 by exposure to UV light (254 nm wavelength) using a low-pressure mercury lamp (shown in Fig. 1). The resolution test chart (37-539, Edmond Optics) made of a fused silica substrate with high UV transmittance provides the line pattern exposure with the spatial frequency in the range of 7.5–3300 lp/mm (line pairs per mm, resolution: 66.7–0.3 μm). The OD value of the line pattern in this UV-exposed area is 0.75. This OD value can be converted to a dose equivalent of 163 Gy using the dose-response fitting for HD-V2 measurements with GT-X980.²⁴ 

The MTF with a resolution test chart using HD-V2 was evaluated using the “Fourier method,³²” in which a square wave is Fourier analyzed to extract a sine wave (the fundamental wave component) and the MTF is calculated from their amplitude ratio. In this analysis, the amplitude of the fundamental wave component as the input square wave is the input amplitude A₀. When the amplitude measured at each spatial frequency is A(n), the MTF for each spatial frequency is $MTFn=A(n)/A0$⁠. When the OD value in the UV-unirradiated region is L and the OD value in the uniformly UV-irradiated region is H, the input amplitude used to calculate the MTF is given by A₀ = 2/π(H − L) in this evaluation of HD-V2. Figures 2(a)–2(c) show the measurement results of the resolution test chart using HD-V2 at 7.5, 17.0, and 24.0 lp/mm scanned by GT-X980 (6400 dpi). When measuring data containing high-frequency components (fine bar patterns), such as in Fig. 2(c), a higher level of spatial resolution is necessary to reproduce them with high accuracy. As the spatial frequency increases, the ability to reproduce the image decreases, and blurred patterns and line widths become indistinct, known as the roll-off effect. In other words, the MTF represents the system’s ability to preserve contrast and resolve details at different frequencies. A significant decrease in the MTF at higher frequencies indicates a decrease in resolution and blurring of high-frequency details. Figures 2(a′)–2(c′) show the line profiles of the red dashed lines in Figs. 2(a)–2(c). The gray dashed lines are the OD values (L) that are UV-unexposed and the OD values (H) that are uniformly UV-exposed. Since the line patterns are transferred by UV light with uniform spatial distribution, the line profile is ideally observed as a square wave. The measurement results are blurred by the system response of GT-X980 and the transmitted light characteristics of the HD-V2, and the amplitude of each spatial frequency also decreases with increasing spatial frequency. The MTF is calculated by measuring line profiles, such as those in Figs. 2(a′)–2(c′), from line patterns of 7.5–50 lp/mm [shown in Fig. 2(d)]. In many cases, the spatial frequency of an MTF >0.1 is defined as the spatial resolution of the optical system. However, when evaluating the quantitative performance as a dosimeter, a high MTF is important, not only the ability to discriminate structures. In this study, the spatial frequency with an MTF >0.8 is specified as the effective resolution, so from the MTF results shown in Fig. 2(d), the spatial resolution of GT-X980 is estimated to be about 6 cycles/mm (83.3 μm).

The spatial resolution of HD-V2 with GT-X980 was evaluated from the MTF, with contrast loss occurring at resolutions below ∼80 μm. This means that the diagnostic performance of the HD-V2’s quantitative coloration will be degraded below this limit of resolution.

It makes sense that this spatial resolution limitation is due to artifacts such as scattering of HD-V2 transmitted light and “orientation effects” that limit spatial resolution^25,26,28 and the hardware limitations of GT-X980. These problems will be solved by using a microdensitometer. In the method of measuring the OD of a film with a microdensitometer, the film is probed with a micrometer-focused light source, and most of the light transmitted through and scattered from the film is focused by a high NA objective lens. The light is then measured by a single detector that reads only one pixel, so there is no mixing of the scattered light with signals from adjacent pixels. In order to evaluate the performance, a test bench for HD-V2 measurements is constructed with a microdensitometer. Since commercial microdensitometers provide high spatial resolution in only one dimension, we developed a microdensitometer with micrometer spatial resolution in two-dimensions.

The TBMD constructed in this study is shown in Fig. 3(a). A continuous-wave helium–neon (HeNe) laser with a maximum output power of 5 mW at a wavelength of 632 nm is used here as an illuminating light source. Note that the active layer of HD-V2 is not affected by the exposure of mW-class HeNe laser.³³ 

The illuminating light is shaped into a Gaussian beam (TEM₀₀ mode) by a spatial filter consisting of objective lens1 (10×/0.25) and a pinhole of φ = 100 μm. In addition, this light is collimated to φ = 5 mm by lens1 (f = 350 mm) and focused by lens2 onto the active layer of HD-V2. For evaluating the performance of the TBMD, three different lenses with focal lengths of f = 75, 150, and 200 mm are used for lens2. Figure 3(b) shows a typical laser focal point position (FPP). The bright central region is called the “airy disk,” and the concentric rings around it are called the “airy pattern.” Note that the airy pattern is removed by adjusting the aperture diameter because it reduces the spatial resolution of the TBMD. The FPP on the active layer is detected by objective lens2 (20×/0.40; f = 10 mm) and lens3 (f = 800 mm) at the aperture position in front of the power sensor (S120C Silicon Photodiode from Thorlabs). The focal diameter with three lenses (f = 75, 150, and 200 mm) is measured by the knife-edge method. The focal diameters, φ, for focal lengths f = 75, 150, and 200 mm were 13.0, 24.4, and 35.6 μm, respectively, as shown in Fig. 4. The theoretical diffraction limit, φ_t, of the focal diameter is calculated by φ_t = 1.22fλ/nφ₀, where n is the refractive index of the medium and φ₀ is the collimated beam diameter before focusing. φ_t is 11.6, 23.2, and 30.9 μm, respectively, and these results mean that the light can be focused with an accuracy of +5% to +15% of the diffraction limit. HD-V2 is mounted on a two-dimensional automated stage and scanned in steps of a minimum of 1 μm.

Thirteen test HD-V2’s exposed to 50–4000 μJ/cm² UV light for the OD response were measured using the TBMD. The three focal diameters (13.0, 24.4, and 35.6 μm) were used to investigate the effect of the HD-V2 monomer structure on the stability of the OD values. A 2 × 2 mm² region of interest (ROI) at the center of each HD-V2 was measured at a pitch of 100 μm, and the output signal I was converted to the OD using Eq. (2).

The MTF with the TBMD is obtained from the resolution test chart used for HD-V2 described in Sec. II A to evaluate the spatial resolution. A focal diameter of 13 μm is selected in the TBMD and moved 1 µm in the X–Y direction using a stepping motor to obtain the minimum measurement limit. Figure 7 shows the results of a two-dimensional spatial distribution of the resolution test chart used for HD-V2 at 24 lp/mm measured with the TBMD [Fig. 7(a)] and with GT-X980 set to 6400 dpi [Fig. 7(a′)]. Figures 7(a) and 7(a′) show that the line patterns are sharper on the TBMD than on GT-X980. The line profile of the red dashed area in Fig. 7(a) is shown in Fig. 7(b). The gray dashed lines in Figs. 7(b) and 7(b′) are the OD mean (L) that is UV-unexposed and the OD mean (H) that is uniformly UV-exposed, obtained with the TBMD and GT-X980. The dashed orange line is the “standard deviation of the OD of the colored area of the resolution test chart used for HD-V2” for the case measured with the TBMD, and the dashed yellow-green line is the “standard deviation of the OD of the area not exposed to UV light.” Ideally, the OD value of the line profile would be constant without variation. Practically, however, variations occur due to the randomness caused by the surface roughness of HD-V2 and the coloration of the polymer. In the measurement, the amount of variation is approximately the same as the standard deviation of the measurement error.

Figure 8 shows the MTF of the TBMD (red) and GT-X980 (black) using the same procedure as in Sec. Ⅱ B. Line pairs of 7.5, 10, 24, 35, 50, 60, 85, 105, 170, and 210 lp/mm of the test HD-V2 are used for the MTF. The TBMD has an MTF of ≥ 0.8 up to about 42 cycles/mm (11.9 µm). Compared with GT-X980, which has an MTF of ≥0.8 of 6 cycles/mm, the spatial resolution of the TBMD is much better than that of GT-X980.

For the discussion of the variation (standard deviations) in the OD values of HD-V2 in Sec. III C (Fig. 6), histograms of the OD values measured with the TBMD are shown in Figs. 9(a)–9(d). These are obtained from a random sampling of HD-V2 (0, 24.4, 205.3, and 898.5 Gy equivalent) at 13, 24.4, and 35.6 μm focused spot diameters. If variations in OD values are caused by stochastic inhomogeneities on the surface state of HD-V2, the standard deviation should decrease as the focal diameter increases. These stochastic inhomogeneities include the inhomogeneity of the coloration of the monomer in the sensitive layer, the physical surface roughness of the sensitive layer, and so on. However, the variations in the OD values of HD-V2 show this tendency at low doses [Figs. 9(a) and 9(b)], but there is no correlation between the focal diameter and standard deviation at high doses [Figs. 9(c) and 9(d)].

The relationship between focused spot diameters and variations in these low-dose HD-V2’s can be explained theoretically using a model of the two-dimensional OD distribution with the measured OD histogram as a reference. The model of the two-dimensional OD distribution is created by using OD histograms (probability density function) obtained from measurements with a focused spot diameter of 13 μm for each HD-V2. Each pixel region of these models is randomly colored with OD values that follow this probability density function and is separated by 13 × 13 μm² intervals/pixel. By adjusting the readout pixel size in this model, we perform Monte Carlo simulations of the TBMD measurements for different focal diameters. This simulation is a simple model to clarify the relationship between the spot diameter and the variation and does not take into account the nonlinear behavior that occurs in the high-dose region. If the experimental results agree with the results of this simulation, the variation is due to the stochastic inhomogeneity of the surface conditions of HD-V2. In other words, if they do not agree, nonlinear effects other than the surface conditions make sense as the major factors generating the variation.

In this simulation, the OD random values are generated from the probability density distribution using the Neumann rejection method, and their OD random values are placed in a two-dimensional array. The simulated OD histogram is obtained by sampling (N = 2500) these OD arrays at 1 × 1, 2 × 2, and 3 × 3 readout pixel sizes (corresponding to 13 × 13, 26 × 26, and 39 × 39 μm², respectively). The OD values in each readout pixel size are averaged. The simulation results are shown in Figs. 9(a′)–9(d′). The reference red lines for each dose in the measured [Figs. 9(a)–9(d)] and simulated [Figs. 9(a′)–9(d′)] results are consistent in the distribution. At low doses, the peak of the measured distribution tends to be lower than the simulation results, but the tendency to follow a stochastic distribution with smaller variations in OD values as the focused spot diameter increases was reproduced. Figures 9(a″) and 9(b″) show the relationship between the readout area and standard deviation. The variations in the measured standard deviation for low-dose HD-V2 agree with the variation curve calculated by simulation. On the other hand, the variations in the measured standard deviation at high doses are not in agreement with the simulations [shown in Figs. 9(c″) and 9(d″)]. The distribution of these focused spot diameter-independent histograms indicates that some physical effect other than the probability coefficient is making a significant contribution.

The physical contribution is discussed by the image profiles [shown in Figs. 10(a)–10(c)] observed at the power sensor position in the TBMD system. Figure 10(a) shows the image profile without HD-V2, where the airy ring outside the white dashed line is removed by the aperture in front of the power sensor. The profile corresponding to 898.5 Gy [Fig. 10(c)] has a more disturbed airy ring shape and degraded imaging performance than 24.4 Gy [Fig. 10(b)]. This degradation in imaging performance has the potential to make the output signal distribution of the profile non-uniform and increase variations in the signal measured by the power sensor. This may be due to the larger effect of probe light scattering when measuring high doses of HD-V2. In transmission type RCF measurements, Schoenfeld et al. had already found that the scattering angle of the transmitted light increases as the dose equivalent increases.²⁸ This increase in the scattering angle disturbs the profile and can cause instability in the light output signal incident on the power sensor.

The stochastic coloration variations in the monomers are convolved with the optical variation due to the scattering caused by each amount of coloration, resulting in the final OD value of the RCF measurements. This suggests that when the dose equivalent is small, the effect of stochastic variations is significant while as the dose equivalent increases, the structural effects of the RCF and the densitometer optics are largely responsible. In the TBMD system, the imaging performance is degraded when measuring HD-V2 of a high-dose equivalent, which increased the amount of coloration and variation in the OD value. To reduce this variation, an objective lens with a large numerical aperture (NA) must be used to improve the focusing characteristics of the transmitted light.

We evaluated the resolving powers of two readout devices, a commercial flatbed scanner (GT-X980) and a developed microdensitometer, when reading image information recorded on a radiochromic film (HD-V2) by using the MTF. The lower limit of the spatial resolution at high contrast on the flatbed scanner (GT-X980) was about 83.3 μm, and it was about 11.9 μm with the developed microdensitometer. The GT-X980 is beneficial in analyzing over several hundred μm in a wide region of interest (ROI), while the microdensitometer is advantageous in terms of resolving fine structures of several tens of micrometers in a relatively small ROI. For example, the emittance measurement of ion beams generated by laser-driven acceleration has to be performed using HD-V2 and the densitometer. We discussed that the variation in optical density when measuring HD-V2 with a developed microdensitometer is a convolution of the variation due to HD-V2 structures and the variation due to the performance of the optical system.

This work was supported by the JST-Mirai Program (No. JPMJMI17A1) and Grants-in-Aid, KAKENHI (Grant Nos. 21J22132 and 22K14021).

The authors have no conflicts to disclose.

Tatsuhiko Miyatake: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Visualization (equal); Writing – original draft (lead). Sadaoki Kojima: Conceptualization (equal); Data curation (supporting); Investigation (supporting); Resources (equal); Writing – original draft (supporting). Hironao Sakaki: Conceptualization (equal); Investigation (supporting); Methodology (equal); Validation (equal); Writing – original draft (supporting). Thanh-Hung Dinh: Data curation (supporting); Methodology (equal); Resources (equal); Writing – review & editing (equal). Ibuki Takemoto: Data curation (supporting); Investigation (supporting); Software (equal); Visualization (equal). Masayasu Hata: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Writing – review & editing (equal). Masaharu Nishikino: Funding acquisition (equal); Project administration (equal); Validation (equal). Yukinobu Watanabe: Resources (equal); Validation (equal); Writing – review & editing (equal). Masahiko Ishino: Project administration (equal); Resources (equal); Software (supporting). Michiaki Mori: Methodology (supporting); Resources (equal); Validation (equal). James Kevin Koga: Investigation (supporting); Validation (supporting); Writing – review & editing (equal). Yoichi Yamamoto: Data curation (supporting); Methodology (supporting); Resources (supporting). Fuyumi Ito: Data curation (supporting); Methodology (supporting); Resources (supporting). Masaki Kando: Funding acquisition (equal); Project administration (equal); Writing – review & editing (equal). Toshiyuki Shirai: Funding acquisition (equal); Project administration (equal); Resources (supporting). Kiminori Kondo: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.