Hello everyone,
I have made several optical phantoms with different weight ratio of ink into PDMS, from 0wt% to 5wt%. I have measured the transmission (%) and reflection (%) of each sample.
From there I calculated the absorption with the Beer-Lambert law, A=log(I0/I), with I0 being the transmission with 0wt% of ink and I the transmission of the sample desired.
I can therefore get the absorption coefficient of the phantoms with the formula: ua = A/thickness.
Therefore I have a linear relationship between the weight percentage of the phantoms and their absorption coefficient.
Now my issue is that I want to create a phantom of 2cm thickness but with a ratio of ink to PDMS known.
Should I assume the absorption coefficient will not change from the 2mm sample to the 2cm one ?
Otherwise, how do I determine the absorption coefficient of my new phantom?
Of course, I cannot measure the transmission of this sample as it is too thick now.
Thank you for your help!
Determining the optical properties of a phantom with a different thickness based solely on the properties of a thinner phantom can be challenging. While there might be some assumptions and approximations involved, I can provide you with some guidance on how to approach this issue.
Firstly, it is important to note that the Beer-Lambert law assumes a linear relationship between the absorption coefficient and the thickness of the medium. However, this assumption may not hold true for all materials and scenarios. In your case, the ink-PDMS mixture might exhibit nonlinear behavior as the thickness increases, especially if there are scattering effects or other factors involved.
To estimate the absorption coefficient of your new 2cm-thick phantom with a known ink-PDMS ratio, you can consider the following approaches:
1. Use a calibration curve: Based on the linear relationship you have established between the weight percentage of ink and the absorption coefficient in the 2mm-thick phantoms, you can create a calibration curve. Plot the weight percentage of ink against the corresponding absorption coefficient for your various samples. Then, extrapolate the calibration curve to estimate the absorption coefficient for the 2cm-thick phantom at the desired ink-PDMS ratio. However, keep in mind that extrapolation introduces additional uncertainties, and the accuracy of the estimation may vary.
2. Consider theoretical models: Explore theoretical models or empirical equations that relate the absorption coefficient to the material composition, such as the Mie theory or effective medium approximations. These models take into account the composition and structure of the material and can provide estimations of the absorption coefficient for different thicknesses. However, the accuracy of these models depends on the specific characteristics of your ink-PDMS mixture.
3. Conduct additional experiments: While it may not be feasible to directly measure the transmission of the 2cm-thick phantom, you could consider alternative experimental methods or techniques that can provide insights into the optical properties. For example, you could use diffuse reflectance spectroscopy, which measures the reflectance of light from the surface of the phantom. By analyzing the reflectance data, you may be able to infer certain optical properties, including the absorption coefficient.
In any case, it is important to acknowledge the limitations and uncertainties associated with estimating the optical properties of a phantom with a different thickness based on data from a different thickness. Ideally, conducting experimental measurements on the 2cm-thick phantom would provide the most accurate and reliable results. However, if that is not possible, the approaches mentioned above can serve as initial estimations, but they may require further validation and verification.
If you need a more detailed approach or further guidance regarding estimating the optical properties of your 2cm-thick phantom based on the known ink-PDMS ratio, please feel free to reach out to me via email at [email protected]. I will be more than happy to assist you in exploring additional strategies or discussing specific theoretical models that could be relevant to your specific case.
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