Relative optimized linearization for radiochromic film dosimetry with non‐uniformity correction

Abstract

Background

Traditional radiochromic film dosimetry requires batch‐specific dose‐response curve measurements, which are time‐consuming and add complexity to clinical workflows. While relative dosimetry techniques have been proposed to streamline the process, they have neglected film non‐uniformities, limiting their accuracy.

Purpose

To develop and validate a relative optimized linearization (ROL) method for radiochromic film dosimetry that eliminates the need for dose‐response curve measurements while incorporating non‐uniformity corrections for improved accuracy.

Methods

The accuracy of the linearization method proposed by Devic et al. was first evaluated through simulations using EBT4 film dose‐response data, with maximum dose values ranging from 1 to 10 Gy. Based on these results, the linearization was refined with an optimized power function to reduce errors across all dose ranges. The optimized linearization was then integrated into the multichannel dosimetry (MCD) framework of Micke et al. to correct for dose‐independent variations, forming the ROL method. ROL was validated against MCD using measured film data from open field, wedge field, and volumetric modulated arc therapy (VMAT) plans. To assess robustness, the VMAT test case was further evaluated under induced positional and dose delivery errors. Sensitivity to treatment planning modeling errors was also examined.

Results

Simulations showed that optimized linearization using ROL reduced average errors from up to 3% in the green channel and 2% in the blue channel to below 1% across all channels and dose ranges. ROL produced dose distributions comparable to MCD (within 1%), particularly in the open and VMAT fields. Only small regions in the wedge field, specifically in the toe region, exceeded 1%, but remained below 1.5%. Sensitivity tests confirmed ROL's robustness to spatial errors and to more subtle treatment planning variations in MLC modeling. Partial plan deliveries, which effectively scale the measured dose distribution, showed expected deviations from MCD. However, gamma analysis of the ROL‐computed dose successfully detected the partial delivery error.

Conclusions

The ROL method provides an efficient alternative to traditional film dosimetry by removing the need for time‐consuming calibration curves while maintaining high accuracy through non‐uniformity corrections. Its streamlined workflow makes it particularly valuable for routine clinical quality assurance.

1. BACKGROUND

Radiochromic film (RCF) dosimetry ¹ has become a widely adopted tool in radiation therapy due to its weak energy dependence, ² near‐tissue equivalence, ³ and high spatial resolution. ⁴ It is commonly used to verify dose distributions in patient‐specific treatment plans and for quality assurance (QA) of medical linear accelerators (LINACs). ⁵ , ⁶ , ⁷ , ⁸ RCF darkens in response to radiation, with the degree of darkening dependent on the absorbed dose, enabling high‐resolution dosimetry. ⁹

The recommended use of RCF requires careful batch‐specific calibration to convert pixel values to dose ¹⁰ , ¹¹ , ¹² , ¹³ and account for dose‐independent variables. ¹⁴ Micke et al. ¹⁵ introduced a multichannel dosimetry (MCD) method that utilizes all three color channels to compute dose while correcting for local variations, such as thickness inconsistencies, unrelated to the delivered dose. Micke et al. proposed that the dose for each channel can be expressed as:

$$D_{c,i}={\mathcal{F}}_c^{-1}({\text{scanOD}}_{c,i}·V_i)$$ (1)

where $D$ is the computed dose, ${\mathcal{F}}^{-1}$ is the inverse of the dose‐response function, scanOD is the scanned optical density defined below, $V$ is the local dose‐independent variation (e.g., non‐uniform film thickness, scanner response), and the subscripts $c$ and $i$ indicate the color channel and the pixel location in the image, respectively.

Micke et al. used the following definition for scanned optical density, where pixel values are normalized to the maximum value of the scanner's 16 bit output:

$${\text{scanOD}}_{c,i}=\log \left(\frac{65535}{P{V}_{c,i}}\right)$$ (2)

where $P{V}_{c,i}$ is the pixel value at location $i$ and color channel $c$. The dose‐response curve is generated by delivering known doses to films and measuring the scanner's optical density as a function of dose over a sufficiently large region of the film to average out dose‐independent variations. Once the dose‐response curve fitting parameters are determined, the variation signal can be determined through optimization, assuming dose independence across channels. The cost function for this optimization is expressed as:

$$\sum _{j\ne k}{\left(D_{i,j}-D_{i,k}\right)}^2\to {\min }_{V_i}.$$ (3)

where $D_i$ represents the dose at a pixel location $i$, $V_i$ denotes the variation at that same location, and $j$ and $k$ index the three color channels: red, green, and blue.

After determining the variation value for each pixel in the scanned film image, it can be removed to calculate the dose using Equation 1, with the optical density adjusted by dividing out the variation value. Shortly after the MCD technique was introduced, Lewis et al. ¹⁰ refined it by incorporating calibration film patches with measurement films in a single scan, reducing environmental and interscan variability. For the remainder of this work, we will refer to the combined one‐scan MCD technique simply as MCD.

While effective, the MCD approach requires time‐consuming calibration curves and additional patches for the one‐scan method, adding complexity to clinical workflows. To simplify this process, Devic et al. ¹⁶ introduced a relative dosimetry method that eliminates the need for both traditional calibration curves and one‐scan patches by employing the following scalable pixel‐to‐dose linearization function:

$$D_{c,i}=a·\frac{{\text{netOD}}_{c,i}^p}{\ln ({\text{netOD}}_{c,i})},$$ (4)

where $D$ is the computed dose, netOD is the measured film net optical density, $p$ is a fixed value of 2/3, and $a$ is a scaling or normalization factor common to relative dosimetry techniques such as film, detector arrays, or ion‐chamber scans such as PDDs or profiles. Devic et al. used the net optical density representation, where each pixel is normalized not by the maximum scanner output value, but by the pixel value of an unexposed film:

$${\text{netOD}}_{c,i}=\log \left(\frac{P{V}_{c,unexp}}{P{V}_{c,i}}\right)$$ (5)

where the indices $i$ and $c$ represent the pixel location in the image and the color channel, respectively, and $P{V}_{c,unexp}$ is the averaged pixel value over a region of interest from an unexposed piece of film from the same batch as the exposed film.

Once linearized, the result is scaled based on the expected dose, as is typical in relative dosimetry. ¹⁷ While this approach simplifies converting a film image into a dose map, it sacrifices accuracy by ignoring dose‐independent variations, which can result in errors as large as 6%, ¹⁸ thus limiting its utility for situations where accuracy is critical. Additionally, it was only demonstrated to be accurate at a specific dose range of 4 Gy, with no data confirming its applicability across lower or higher doses.

An ideal solution would involve a sufficiently robust relative dosimetry technique that can also correct for dose‐independent factors, providing a balance between accuracy and efficiency. In this work, we propose computing the variation maps for non‐uniformity correction without dose‐response curves. This is accomplished by first improving the accuracy of existing linearization techniques and then by replacing the dose‐response function (${\mathcal{F}}^{-1}$ in Equation 1) with the new improved linearization. This allows for the cost function in Equation 3 to be cast solely via relative film dosimetry techniques.

2. METHODS

2.1. Relative optimized linearization

To achieve the most accurate variation values for removing non‐uniformities, the optimization in Equation 3 requires accurate dose computations across all three color channels. To this end, we propose an improvement to the approach of Devic et al. by introducing a variable power function where the values of $a$ and $p$ in Equation 4 can be determined numerically via optimization using a cost function that evaluates the mean absolute error between the expected and the calculated doses for each color channel:

$$\sum _{i|D_i>\tau }\left|D_i-a_c·\frac{{\text{netOD}}_{c,i}^{p_c}}{\ln ({\text{netOD}}_{c,i})}\right|\to {\min }_{a_c,p_c}$$ (6)

where $D_i$ is the expected dose at pixel $i$, obtained, for example, from a treatment planning system (TPS), ${\text{netOD}}_{c,i}$ is the measured net optical density at pixel $i$ for color channel $c$, and $\tau$ is a minimum dose threshold included to prevent the optimization from disproportionately prioritizing large low‐dose regions outside the radiation field. In this form of the cost function, both the power value $p_c$ and the scaling value $a_c$ are optimized simultaneously for each color channel $c$, resulting in a linearization and normalization that aims to match the measurement to the expected dose across all pixels where the expected dose is above the threshold $\tau$. With regard to the scaling value $a$, this approach differs from traditional normalization methods, such as single‐point maximum value or central‐axis normalization, which are less robust due to potential film non‐uniformity at the normalization point.

This approach will be referred to as relative optimized linearization (ROL) throughout the remainder of this work.

2.2. Evaluation of ROL

The MCD method utilizes all three color channels to account for non‐uniformities that introduce dose‐independent film responses. For this approach to be effective, it is essential that all three channels accurately represent these non‐uniformities so they can be properly corrected in the final result. This requirement may explain why relative dosimetry has not been applied to the film non‐uniformity problem. For example, Devic et al. reported that the red channel may not linearize well at doses exceeding 1 Gy. Moreover, since only the coefficients of determination (R²) for the linear fit were provided, and not the resulting linearization errors, it is difficult to fully evaluate the effectiveness of the technique from this early work.

To assess the feasibility of replacing the MCD method with a relative approach that does not require acquiring dose‐response curves, we first evaluated the accuracy of the linearization method proposed by Devic et al. through simulations based on EBT4 (Ashland Inc., Wayne, NJ, USA) film dose‐response data. This evaluation, which first used the original fixed power value of 2/3, aimed to verify that the linearization process was sufficiently robust ‐ maintaining accuracy within 1% across all three color channels, to provide reliable inputs for optimizing non‐uniformity correction. The simulations were then repeated with optimized (non‐fixed) power value and the results were compared to evaluate the effectiveness of the proposed technique.

The evaluation was based on a simulated one‐dimensional linear dose array, $D_{\text{exp}}$, ranging from 10 cGy to 3 Gy in 3 cGy increments. This uniformly increasing set of dose values was first converted into red, green, and blue pixel values using measured EBT4 dose‐response curves, using the following rational function:

$$\text{scanOD}=\log \left(\frac{a+bD}{c+D}\right)$$ (7)

where scanOD is the scanner optical density determined using Equation 2, $D$ is the delivered dose, and $a$, $b$, and $c$ are the fitting parameters. The fit parameters for this simulation were determined from films irradiated with a 6 MV flattened beam at 0, 25, 50, 75, 100, 150, 200, 300, 400, 500, 800, and 1000 cGy. Pixel values were obtained by averaging regions of interest (ROIs) approximately 2$\times$2 cm in size from each film patch.

All three arrays of pixel values were then transformed into net optical density (netOD) and then linearized using the second term in Equation 4. Scaling factors $a$ for each color channel were then applied to ensure that the maximum linearized netOD for each channel matched the maximum of the original dose profile, yielding the final dose profile $D_{\text{lin}}$. The results were compared to the original dose values to assess the technique's ability to linearize the channel‐specific non‐linear dose‐response of EBT4 film, using global percentage errors (${\epsilon }_i$) computed across all three color channels as follows:

$${\epsilon }_i=\frac{D_{\text{exp},i}-D_{\text{lin},i}}{D_{\text{exp,max}}}\times 100$$ (8)

where $D_{\text{exp},i}$ is the input dose value at location $i$, $D_{\text{lin},i}$ is the output linearized pixel response at location $i$, and $D_{\text{exp,max}}$ is the maximum value in the input dose profile. This simulation was also repeated for a dose profile with maximum dose of 10 Gy. These dose ranges for these two initial simulations were selected to represent a typical clinical QA plan and the maximum dose specified in the EBT4 film datasheet.

While the initial simulations assessed linearization accuracy at specific maximum doses of 3 and 10 Gy, additional simulations were conducted to evaluate robustness across a broader range of maximum dose values, from 2 to 10 Gy in 10 cGy increments. Because the slope of the dose‐response curve varies across the applicable dose range, and the maximum dose is commonly used as the normalization reference, this value has a significant impact on the overall accuracy of the linearization process (as also reported by Devic et al.). For each profile with a different maximum dose, a linearization error profile was computed using Equation 8, and the average error across the entire profile was calculated. This analysis provides a more comprehensive understanding of the method's performance when applied to measured films with varying maximum dose levels.

All data analysis routines were implemented by the authors in Python. ¹⁹

2.3. ROL with non‐uniformity correction

To extend the new ROL technique to correct for dose‐independent non‐uniformities, the optimization framework of Micke et al. (Equation 3) was modified by replacing the dose computed using MCD (Equation 1) with the dose computed using ROL (Equation 4, using optimized values of $a$ and $p$).

$$\sum _{j\ne k}{\left(D_{i,j}^{rol}-D_{i,k}^{rol}\right)}^2\to {\min }_{V_i}.$$ (9)

where $D_{i,j}^{rol}$ is the optimized linearized dose formula modified to incorporate local dose‐independent variations as follows:

$$D_{c,i}^{rol}=a_c·\frac{{\text{netOD}}_{c,i}^{p_c}}{\ln ({\text{netOD}}_{c,i})},$$ (10)

where $a_c$ and $p_c$ are the optimized scale and power values for color channel $c$, and ${\text{netOD}}_{c,i}$ is the corrected net optical density that accounts for local dose‐independent variations at pixel location $i$ and color channel $c$. Here, the netOD represents a crucial step in our method, as it incorporates the non‐uniformity correction (based on scanOD) directly into the relative optimized linearized dose (based on netOD). To compute netOD within this framework, we first convert each raw pixel value to scanner optical density (scanOD) using Equation 2. This scanOD is then corrected for non‐uniformities on a pixel‐by‐pixel basis by multiplying it by the variation value $V_i$. The corrected scanner optical density is then converted back to a pixel value using the inverse of Equation 2, and finally converted to net optical density (netOD) using Equation 5. This corrected netOD (shown in Equation 11 and derived in Appendix A) ensures that the dose‐independent variations are accounted for consistently with the MCD method while being incorporated into our new ROL approach. A flowchart outlining the steps involved in the entire ROL method is shown in Figure 1.

$${\text{netOD}}_{c,i}^{\text{corrected}}={\text{scanOD}}_{c,i}·V_i-{\text{scanOD}}_{c,unexp}$$ (11)

FIGURE 1.

Flowchart of the ROL method, showing the sequential processing steps: (1) Scan the QA film together with an unexposed reference film, (2) Compute netOD for each color channel using Equation 5, (3) Determine the linearization parameters $a$ and $p$ for each channel by minimizing the cost function in Equation 6, (4) Compute scanOD for each channel using Equation 2, (5) Compute the variation map using the scanOD and the linearization parameters from the previous two steps, via optimization with Equation 3 (Equation 11 is applied within the optimization to convert between scanOD and netOD, since the linearization is defined in terms of netOD while the non‐uniformities are corrected using scanOD). (6) Compute the corrected netOD using Equation 11 together with scanODs and the previously determined variation map. (7) Compute the final dose for each channel using Equation 10, the corrected netOD from step 6, and the linearization parameters from step 3.

2.4. Demonstration of technique

To assess ROL's ability to replicate dose distributions produced by MCD, EBT4 film was used to measure dose distributions for three treatment plans: open and wedged 10 $\times$ 10 cm fields, and a volumetric modulated arc therapy (VMAT) plan. The comparison was based on dose‐difference maps between the traditional MCD method and the newly proposed ROL technique across all three color channels.

An open field was chosen as the simplest example to demonstrate the technique's effectiveness. A wedge field was included to evaluate performance in mid‐dose ranges, which are typically obscured within the penumbra. The VMAT plan was selected as a real‐world clinical example to assess the method's applicability.

All plans were created in Eclipse (Siemens Healthineers, Erlangen, Germany), and the expected planar doses were exported in DICOM format. During both plan delivery and calibration, the film was positioned at a depth of 5 cm within a polystyrene slab, with an additional 5 cm of backscatter material placed behind it. The VMAT test plan included two spherical targets positioned approximately 7 cm apart in the coronal plane at isocenter, with diameters of approximately 4 and 5.5 cm. Each target was prescribed a dose of 300 cGy.

Films were scanned using an Epson 11000XL scanner in transparency mode with 16 bits per channel at a resolution of 150 dpi, with all color adjustments disabled. The cross‐plane direction of the film was aligned with the scanner's carriage travel direction. A glass plate was placed over the films to ensure they remained flat during scanning.

The one‐scan method proposed by Lewis et al. ¹⁰ was used to scale the original dose‐response curves, and the triple‐channel non‐uniformity correction method of Micke et al. was subsequently applied. As part of the one‐scan method, two reference films were scanned alongside each QA film: one unexposed and the other exposed to the maximum dose expected in the QA film. Films were physically marked with fiducials based on the room lasers, and these marks were used to register the scanned images. Small registration adjustments were also made in software to optimally align the measured and expected distributions spatially. Ideal spatial coincidence was desired for benchmarking the technique; however, controlled spatial errors were also introduced to assess the method's robustness (see next section). Additionally, different threshold values ($\tau$ in Equation 6) of 1%, 5%, 10% and 15% were evaluated to assess the effect of threshold selection, and to support the selection of a final threshold value for comparing ROL and MCD dose across all test plans.

2.5. Sensitivity to treatment errors

To evaluate the robustness of the proposed method against discrepancies between measured and expected dose distributions, the VMAT test case was repeated with two types of errors: (1) a 3 mm spatial positioning error applied in the cross‐plane direction, referred to as VMAT‐shifted, and (2) a dose delivery error in which the second of the two arcs was prematurely terminated by approximately 25%, referred to as VMAT‐partial. This analysis is critical because the expected dose is used in the cost function to optimize the linearization parameters, and any mismatch between the measured film dose and the expected dose can lead to inaccurate or misleading results. Spatial positioning and dose delivery errors are common in clinical QA tests. The proposed technique would therefore be impractical if the resulting dose distribution were strongly affected by such sources of error. These two scenarios were selected as worst‐case conditions to evaluate the method's robustness under these conditions.

2.6. Sensitivity to planning modeling errors

To evaluate the ability of the proposed ROL method to detect errors arising from incorrect treatment planning modeling parameters, an analysis was performed using a C‐shape test plan based on the AAPM Task Group 119 guidelines. In this case, errors in the MLC modeling, specifically, the dosimetric leaf gap (DLG), were simulated by systematically adjusting the MLC offset in the treatment planning system. This test evaluates the method's sensitivity to beam model discrepancies, such as those introduced during LINAC commissioning or TPS configuration.

The C‐shape plan consisted of a PTV surrounding a central cylindrical core. The PTV was an arc‐shaped structure with an inner radius of 1.5 cm, an outer radius of 3.7 cm, and a length of 8 cm. The central core, which was separated from the PTV by a 0.5 cm margin, was a 1 cm‐radius cylinder with a length of 10 cm. Film was irradiated with a 6 MV flattened beam using a modular film phantom composed of 2 cm‐thick slabs of 15$\times$15 cm ABS material (density: 1.04 g/cm³), with laser‐cut EBT4 film precisely registered within the phantom using a three‐pin registration system.

The plan was based on a synthetic CT dataset, with the origin aligned to the physical center of the film. This ensured accurate origin definition during treatment planning. Irradiations were performed on a Truebeam LINAC (Siemens Healthineers, Erlangen, Germany) with the film positioned in the axial orientation. Setup was performed via CBCT registration and verified using in‐room lasers. No additional shifts were introduced ‐ all analysis was based solely on the geometric accuracy of the CBCT alignment and film registration system.

Dose distributions were calculated using Eclipse v18.0.1.261 (Siemens Healthineers, Erlangen, Germany), with MLC offset values varied from 0.0 to 0.4 mm in 0.1 mm increments. Film registration, including rotation and translation corrections, was executed using custom software based on fiducial markers and phantom pin alignment. Gamma analysis was conducted using a global 2 mm, 3% criterion, with pass rates computed over the region receiving more than 10% of the maximum dose.

While the principal aim was to evaluate the ROL method's sensitivity to small variations in the planning model, we also provided context for the results by conducting a parallel evaluation of gamma pass rates between doses predicted by the TPS and those measured via the MCD technique on the same film. The MCD dose was derived using the same procedure described above which included dose response curves, one‐scan film patches, and computation of variation maps. We then compared gamma pass rates for each MLC offset between the two methods.

3. RESULTS

3.1. Relative linearization without optimization

Simulation results using measured EBT4 dose‐response curves and the original (non‐optimized) linearization method of Devic et al., applied to dose profiles with maximum doses of 3 and 10 Gy, are shown as dashed lines in Figure 2. For the 3 Gy simulation, the blue channel exhibits the largest errors, reaching up to 2% around 1 Gy. In contrast, the red and green channels show relatively low errors, remaining below 1% across nearly the entire dose range. For the 10 Gy simulation, the green channel demonstrates the largest errors, peaking at approximately 5% near 5 Gy. The blue channel shows maximum errors of about 2% around 4 Gy, while the red channel achieves the best linearization, with errors consistently below 1%.

FIGURE 2.

Simulation results for 3 and 10 Gy dose profiles, based on measured EBT4 dose‐response curves. All lines represent the global percentage error between the original input and linearized output doses for each channel. Dashed lines indicate the non‐optimized linearization percent errors, while solid lines depict the optimized results. Each line is color‐coded to match its corresponding color channel.

Repeating this type of simulation with datasets featuring different maximum doses ranging from 1 to 10 Gy yielded the average linearization errors shown as the dashed lines in Figure 3. In this figure, the red channel (dashed red line) exhibits the smallest errors, reaching as low as 0.1% around 7 Gy. The green channel shows its minimum error just below 0.5% near 2 Gy before steadily increasing to 3% at 10 Gy. The blue channel's error gradually increases from approximately 1% at 1 Gy to 2% at 10 Gy.

FIGURE 3.

Average linearization absolute error per channel as a function of maximum dose for EBT4 film across all three color channels for simulations ranging from 1 to 10 Gy. Dashed lines represent non‐optimized linearization, while solid lines indicate optimized average errors.

3.2. Relative linearization with optimization

3.2.1. Simulated profiles

The optimal power and scale values ($a$ and $p$ in Equation 4) for both 3 and 10 Gy simulations for all three color channels are shown in rows 1 and 2 of Table 1. The solid lines in Figure 2 show the results of the optimized linearization for both the 3 and 10 Gy simulations using these optimized values. Compared to the non‐optimized linearization (dashed lines), this approach reduces percentage errors across all dose levels. Similarly, the solid lines in Figure 3 represent the average global percentage errors observed across multiple optimized linearization simulations with maximum dose values ranging from 1 to 10 Gy. These results demonstrate a substantial reduction in errors across all dose values compared to the non‐optimized averages (dashed lines in the same plot).

TABLE 1.

Optimized power ($p$) and scaling ($a$) values for simulations and all test cases.

	$p$			$a$
	Red	Green	Blue	Red	Green	Blue
Sim, 3 Gy	0.690	0.669	0.727	1065.5	1920.8	5940.0
Sim, 10 Gy	0.657	0.531	0.753	1020.8	1498.9	6366.9
Open	0.703	0.678	0.723	1157.0	2096.2	6614.7
Wedge	0.675	0.639	0.691	1128.4	1970.7	6233.6
VMAT	0.762	0.772	1.027	1204.8	2375.9	13 976.3
VMAT‐shifted	0.754	0.769	1.025	1185.5	2352.3	13 813.8
VMAT‐partial	0.730	0.713	0.823	1307.4	2438.0	9175.9

Abbreviation: VMAT, volumetric modulated arc therapy.

3.2.2. Test plans

Measured response curves for EBT4 film were used with the MCD method to compute the planar dose across all three color channels for each film, serving as references to evaluate the effectiveness of the new ROL approach. The optimal power ($p$) and scaling values ($a$) determined for all test fields are shown in Table 1. The computed variation maps for the wedge field, generated using both MCD and ROL, are presented in Figure 4. These results demonstrate that ROL can produce variation maps closely matching those obtained with MCD (open and VMAT variation maps were also very similar between the MCD and ROL methods). The percent difference maps comparing the MCD and ROL doses for all test plans are shown in Figure 5. A threshold of 5% was used for the ROL parameter optimization. This choice was based on the results of the threshold evaluation tests shown in Figure 6, where 5% produced the best agreement between ROL and MCD.

FIGURE 4.

Variation maps generated using both the MCD and the proposed ROL methods for the wedge test plan. MCD, multichannel dosimetry; ROL, relative optimized linearization.

FIGURE 5.

Global percent error maps comparing ROL to MCD computed doses for all three color channels in: (a) open field, (b) wedge field, (c) VMAT plan, (d) VMAT plan with a 3 mm shift, and (e) partially delivered VMAT plan. MCD, multichannel dosimetry; ROL, relative optimized linearization; VMAT, volumetric modulated arc therapy.

FIGURE 6.

Global percent error maps comparing ROL to MCD computed doses for the red color channel for different linearization optimization threshold values ($\tau$ in Equation 6) for all three test plans. MCD, multichannel dosimetry; ROL, relative optimized linearization.

The average absolute error, and standard deviation of the raw error, evaluated within the low‐, middle‐, and high‐dose regions, are shown in Table 2.

TABLE 2.

Average absolute percent error and standard deviation of the raw percent error between MCD and ROL doses for all test plans and color channels, categorized by low‐dose, middle, and high‐dose regions.

Test plan	Channel	Low	Middle	High
Open	Red	0.28 $\pm$ 0.09	0.15 $\pm$ 0.17	0.42 $\pm$ 0.26
	Green	0.50 $\pm$ 0.22	0.37 $\pm$ 0.31	0.63 $\pm$ 0.33
	Blue	0.23 $\pm$ 0.27	0.54 $\pm$ 0.36	0.36 $\pm$ 0.43
Wedge	Red	0.51 $\pm$ 0.14	0.47 $\pm$ 0.35	0.70 $\pm$ 0.31
	Green	0.87 $\pm$ 0.28	0.51 $\pm$ 0.37	0.37 $\pm$ 0.43
	Blue	0.43 $\pm$ 0.26	0.71 $\pm$ 0.42	0.61 $\pm$ 0.42
VMAT	Red	0.16 $\pm$ 0.18	0.20 $\pm$ 0.32	0.18 $\pm$ 0.22
	Green	0.31 $\pm$ 0.33	0.76 $\pm$ 0.33	0.19 $\pm$ 0.24
	Blue	0.32 $\pm$ 0.31	0.66 $\pm$ 0.37	0.38 $\pm$ 0.36
VMAT shifted	Red	0.16 $\pm$ 0.16	0.13 $\pm$ 0.28	0.39 $\pm$ 0.24
	Green	0.32 $\pm$ 0.33	0.79 $\pm$ 0.35	0.39 $\pm$ 0.23
	Blue	0.28 $\pm$ 0.30	0.65 $\pm$ 0.37	0.70 $\pm$ 0.36
VMAT partial	Red	0.92 $\pm$ 0.40	3.43 $\pm$ 1.73	10.19 $\pm$ 0.59
	Green	1.20 $\pm$ 0.41	3.20 $\pm$ 1.51	10.13 $\pm$ 0.71
	Blue	0.72 $\pm$ 0.46	2.98 $\pm$ 1.65	9.81 $\pm$ 0.72

Note: Low dose is defined as below 20%, and high dose as above 80% of the normalized dose range.

Abbreviations: MCD, multichannel dosimetry; ROL, relative optimized linearization; VMAT, volumetric modulated arc therapy.

Dose profiles for the VMAT field, computed using both MCD and ROL, are shown in Figure 7. These profiles demonstrate excellent agreement between the doses calculated with MCD and the proposed ROL technique. Aside from the partial VMAT, similar levels of agreement were observed in the dose profiles for the open and wedge test plans. Profiles for the partial VMAT plan are shown in Figure 8. This figure shows that the MCD dose is, as expected, considerably lower than the planned dose. The ROL relative dose, which is scaled as part of the method, is closer to the expected dose, but inconsistencies are present between the two due to the fact that the plan was partially delivered and not simply scaled in monitor units delivered.

FIGURE 7.

Measured versus expected red channel dose profiles (cross‐plane and in‐plane) through the center of the upper‐right target of the VMAT plan, as indicated by the crosshairs in subplot (a) of Figure 10. The MCD dose is shown in orange, the ROL dose in maroon, and the expected dose from the planning system in gray. MCD, multichannel dosimetry; ROL, relative optimized linearization; VMAT, volumetric modulated arc therapy.

FIGURE 8.

Measured versus expected red channel dose profiles (cross‐plane and in‐plane) through the center of the upper‐right target of the partial VMAT plan, as indicated by the crosshairs in subplot (a) of Figure 10. The MCD dose is shown in orange, the ROL dose in maroon, and the expected dose from the planning system in gray. MCD, multichannel dosimetry; ROL, relative optimized linearization; VMAT, volumetric modulated arc therapy.

3.2.3. Sensitivity to planning modeling errors

Gamma analysis results from the MLC offset sensitivity tests (Figure 9) demonstrate that both MCD and ROL exhibit small but noticeable variations across the different MLC offset values. The corresponding pass rates, summarized in Table 3, indicate that the optimal MLC offset was 0.1 mm for MCD and 0.2 mm for ROL. Notably, the value being used clinically was 0.2 mm.

FIGURE 9.

Red channel gamma analysis maps (3%, 2 mm) generated using both MCD and ROL methods for the axial film measurement of the TG‐119 C‐Shape treatment plan (6 MV), across MLC offset values ranging from 0.0 to 0.4 mm. MCD, multichannel dosimetry; ROL, relative optimized linearization.

TABLE 3.

Gamma pass rates (3%, 2 mm) for varying MLC offset values, as determined using both MCD and ROL methods.

MLC offset (mm)	Gamma pass rate (%)
	MCD	ROL
0.0	99.69	99.34
0.1	99.80	99.35
0.2	99.79	99.39
0.3	99.73	99.35
0.4	99.62	99.35

Abbreviations: MCD, multichannel dosimetry; ROL, relative optimized linearization.

4. DISCUSSION

We have presented a ROL method for radiochromic film dosimetry that eliminates the need for dose‐response curve measurements. This approach introduces an improved linearization formula for pixel‐to‐dose conversion, demonstrating accuracy across the full EBT4 dose range up to 10 Gy. To the best of the authors' knowledge, this is the first relative dosimetry method to incorporate non‐uniformity corrections, which are crucial for achieving high‐accuracy film dosimetry.

The results from the simulations performed provide insight into the average linearization errors that can be expected from ROL as a function of the maximum dose delivered to the film. For example, the results shown in Figure 3 demonstrate that the red channel maintains a low average error of less than 0.25% across all maximum dose levels. The blue channel exhibits higher average errors at lower doses but approaches the red channel's performance around 4 Gy. In contrast, the green channel shows a roughly linear increase in average error with increasing maximum dose, though it remains below 1% even at 10 Gy.

This behavior stands in contrast to the non‐optimized linearization, where the accuracy is more sensitive to the maximum dose, and this sensitivity can vary by film type. For instance, Devic et al. reported that linearization for EBT2 and EBT3 films resulted in inaccuracies in the red channel when the maximum dose exceeded 1 Gy. To confirm this, we ran additional simulations using published EBT3 dose‐response curves and observed similar trends: the red channel showed the largest errors, with maximum deviations around 4% at 2 Gy, increasing to 7% at 10 Gy. In contrast, the EBT4 non‐optimized simulation results presented here in Figure 3 show excellent red channel linearization (< 1% error), with the green channel steadily increasing above 3 Gy and reaching as high as 3% (see dashed green line). Most importantly, by introducing optimization into the linearization process, this sensitivity to maximum dose is effectively eliminated, with all channel errors remaining below 1% regardless of the dose range. Future work could explore whether this holds true for EBT3 as well, though given that product's approaching end of commercial life, this may not be a critical priority.

We evaluated the ROL technique by comparing it with established multichannel dosimetry across all color channels for various test cases, including open and wedge fields, as well as a VMAT plan. The results demonstrated that the proposed ROL method successfully solved for the linearization parameters, yielding optimized power values ranging from 0.531 to 1.027. While these values deviate from the fixed exponent of 2/3 proposed in the earlier work that motivated this study, they remain within a similar range, suggesting that a variable power offers improved flexibility and accuracy across different dose distributions.

The ROL technique demonstrated the ability to produce variation maps comparable to those generated by MCD (see Figure 4), as well as final dose distributions corrected for non‐uniformities (see Figure 5). This is an important result, as it was not initially clear that the linearization optimization process, used to independently determine the best linearization parameters for each color channel, would yield color channel outputs suitable for accurate variation map computation. The pixel‐level agreement between MCD and ROL doses is clearly illustrated in Figure 7, where the dose profiles from both methods closely match across the field in both the in‐plane and cross‐plane directions. This strong correlation, observed consistently across all test plans, would not have been possible if the ROL technique were unable to correctly determine variation maps to account for non‐uniformities. The ability of ROL to match MCD in this respect is a key finding of this work.

As shown in Figure 5, the red channel demonstrated the best overall agreement between MCD and ROL, with errors generally remaining below 1%. The average error values presented in Table 2 further support this observation: aside from the wedge test, the red channel consistently shows lower average errors and standard deviations across all test plans. The wedge test appearing as an outlier is not unexpected, as it was intentionally selected to evaluate the accuracy of the optimized linearization across a broad range of dose values. In contrast, the open and VMAT plans exhibit a more distinct separation between low‐ and high‐dose regions, which allows the optimization process to more easily match those dominant areas. When dose values are well separated, the algorithm can focus on fitting two primary dose levels. However, when the dose values are more uniformly distributed, such as in the wedge test, it becomes more challenging to find a linearization that accurately fits the entire range. Even in this worst‐case scenario, the red channel differences between MCD and ROL remain below 2%, with discrepancies limited to small regions in the toe area of the wedge field.

A minimum dose threshold was introduced into the linearization optimization cost function shown in Equation 6. Without this threshold, the size of the measured film was found to influence the results, as larger films contained a greater number of out‐of‐field pixels. The evaluation of different threshold values, shown in Figure 6, indicated that a 5% threshold was optimal. This threshold effectively excluded pixels just outside the lower transition portion of the penumbra, resulting in more robust and accurate optimization. The threshold selection had little to no noticeable effect on the VMAT plan analysis, which was attributed to the fact that, unlike the open and wedge plans, the VMAT‐delivered film had a much lower percentage of pixels below the threshold values. As a result, the optimization was already insensitive to their contribution.

The sensitivity tests demonstrated that ROL performs well in the presence of spatial positioning errors between the expected and measured dose distributions. This is evident from the similarity of the gamma maps shown in subplots (c) and (d) of Figure 10, which show pass rates of 82.92% and 82.95%, respectively. In contrast, ROL fails to produce a dose distribution similar to MCD when a partial plan is delivered. This discrepancy arises because a partially delivered plan results in a lower measured dose distribution, which is then scaled up to match the expected dose as part of the ROL technique. This scaling causes the MCD and ROL doses to diverge, as can be seen in Figure 8. While this is expected, since relative 2D dose measurements cannot detect dose scaling errors, it is still potentially concerning, as clinical usefulness would require ROL to detect treatment delivery errors that are not simply the result of MU scaling.

FIGURE 10.

Gamma analysis maps (3%, 2 mm) for VMAT expected dose compared against (a) fully delivered film analyzed with MCD, (b) fully delivered film analyzed with ROL, (c) shifted film analyzed with MCD, (d) shifted film analyzed with ROL, (e) partially delivered film analyzed with MCD, and (f) partially delivered film analyzed with ROL. The crosshairs in (a) indicate the location of the profiles shown in Figure 7 and Figure 8. MCD, multichannel dosimetry; ROL, relative optimized linearization; VMAT, volumetric modulated arc therapy.

To rule out the possibility that ROL might have produced a dose distribution sufficiently similar to the expected dose, potentially causing a clinical QA test to overlook the partial delivery, the authors computed gamma analysis maps for the partial VMAT plan using both the MCD and ROL dose distributions (see subplots (e) and (f) of Figure 10). Even though the ROL dose, which is scaled to match the expected dose, has a higher gamma pass rate than the MCD, the ROL gamma map clearly indicates a failure. The gamma pass rates (3%, 2 mm, 10% threshold) for the partial VMAT tests were 65.6% and 92.7% for MCD and ROL, respectively. This result confirms that both MCD and ROL are capable of detecting the partial delivery, as the pass rates are substantially lower than those observed for the fully delivered VMAT plan (99.5% for MCD and 99.3% for ROL).

Similar trends were observed when small changes were introduced into the treatment planning model. The ROL method was able to resolve differences in DLG values based on variations in MLC offset, indicating that its output reflects sensitivity to the underlying model parameters rather than simply conforming to the expected dose distribution used during optimization. Notably, the MCD results suggested an optimal MLC offset of 0.1 mm, whereas the parallel analysis using ROL methods identified 0.2 mm as optimal, which matched the value previously determined and used clinically by the local physics team in their treatment planning system.

At this stage, the authors do not recommend that ROL be used as a replacement for established methods of determining DLG parameters. ²⁰ Instead, these findings, together with the other sensitivity tests presented, are intended to provide a broad overview of the behavior and characteristics of the ROL optimization process being introduced. These sensitivity findings collectively support a key conclusion regarding ROL: despite incorporating an optimization process to derive dose from scanned pixel values, the method lacks sufficient degrees of freedom to force the measured dose to match the expected dose. The optimization is constrained to adjusting the linearization function and a global scaling factor and it therefore cannot arbitrarily deform or reshape the dose distribution to align with expected values.

To further verify that the ROL optimization did not produce unintended results, the similarity between ROL and MCD dose distributions for the partial VMAT plan was evaluated, aside from a global scaling factor. This was assessed by normalizing the ROL doses to the MCD doses, revealing excellent agreement–within 1% in‐field and 2% out‐of‐field. This tendency to obscure scaling errors is an important limitation to consider when using any relative 2D dosimetry technique. Future work could include exploring a broader range of treatment delivery errors, both in type and magnitude, and determining whether gamma analysis of ROL‐processed films would successfully detect them.

While the ROL method shows strong agreement with established multichannel dosimetry across a variety of test plans, it is important to note that it is not intended to serve as an independent method for absolute dose validation, which should never be the role of a relative dosimetry technique. As expected, ROL cannot detect global dose scaling errors, such as those resulting from LINAC output miscalibration, since the optimization process inherently scales the measured film dose to match the expected distribution. However, when the expected discrepancies are more subtle, relative techniques like ROL may be particularly well‐suited, as they are less affected by global uncertainties in machine calibration. In these cases, ROL can better highlight localized spatial inconsistencies or delivery errors that might otherwise be masked. This is not a unique characteristic of the newly developed method, but rather a fundamental property of all relative dosimetry techniques that involve some form of measurement scaling typically derived from an expected dose distribution.

A suitable clinical use case for ROL is routine QA of patient‐specific planar dose distributions, where measured film is compared to the expected dose from the TPS, provided that baseline pass rates have been established using MCD during the TPS commissioning and validation process. Another valuable application is the evaluation of subtle changes in dose distribution resulting from modifications to the treatment planning dose model, where ROL can help isolate the dosimetric impact of specific parameter adjustments.

From a clinical implementation standpoint, ROL offers practical advantages, especially in busy clinics with limited resources. Traditional multichannel dosimetry workflows require time‐intensive preparation: generating and analyzing dose‐response curves for each film batch, performing calibration irradiations, scanning multiple films, and ensuring consistent scanner placement and orientation. Errors introduced by misaligned film placement or inconsistent scanning procedures have been reported in the literature, ¹⁴ , ²¹ emphasizing the complexity of current workflows.

The ROL method eliminates the need for batch‐specific dose‐response measurements and one‐scan calibration films. Instead, it requires only that an unexposed film from the same batch be scanned and analyzed alongside the QA film. This relative approach simplifies the process, reduces the potential for operator error, and streamlines QA film analysis, making it particularly attractive for high‐throughput clinical environments.

5. CONCLUSION

The methods presented here offer an accurate and efficient approach for converting measured radiochromic film optical density to dose using relative techniques, simplifying the film dosimetry process by eliminating the need for time‐consuming calibration curves.

CONFLICT OF INTEREST STATEMENT

Nicholas Zacharopoulos is employed by Aktina Medical Corp.

APPENDIX A. DERIVATION OF NON‐UNIFORMITY CORRECTED NET OPTICAL DENSITY

$$\begin{array}{cc}\hfill {\text{netOD}}_{c,i}^{\text{corrected}}& =\log \left(\frac{P{V}_{c,\text{unexp}}}{P{V}_{c,i}^{\text{corrected}}}\right)\hfill \\ & =\log \left(\frac{P{V}_{c,\text{unexp}}·{10}^{{\text{scanOD}}_{c,i}{V}_i}}{65535}\right)\hfill \\ & =\log (P{V}_{c,\text{unexp}})+{\text{scanOD}}_{c,i}·V_i\hfill \\ & -\log (65535)\hfill \\ & ={\text{scanOD}}_{c,i}·V_i+\log \left(\frac{P{V}_{c,\text{unexp}}}{65535}\right)\hfill \\ & ={\text{scanOD}}_{c,i}·V_i-{\text{scanOD}}_{c,unexp}\hfill \end{array}$$ (A.1)

Zacharopoulos NG, Pater P. Relative optimized linearization for radiochromic film dosimetry with non‐uniformity correction. Med Phys. 2025;52:e70012. 10.1002/mp.70012

DATA AVAILABILITY STATEMENT

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