Redbird - Conversion of fluence into diffuse reflectance
Charly Caredda
In this equation, F is the fluence, R_Fres is the Fresnel reflection coefficient for a photon incident at an angle θ relative to the surface normal, D = 1 / [ 3 (µ_a + µ_s')], and dΩ is the solid angle element.
If I understand correctly, the diffuse reflectance corresponds to the integral of the radiance (fluence and flux contributions) over a hemisphere. The flux term is given by the derivative of the fluence along the z-axis. Since the solid angle element is dΩ = sin(θ)dθdφ, I assume the equation can be rewritten as:
Does it make sense?
Thank you so much for your help
:)
Best,
Charly
[1] Alwin Kienle and Michael S. Patterson, "Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium," J. Opt. Soc. Am. A 14, 246-254 (1997)
Qianqian Fang
hi Charly,
as you might have noticed, I updated Redbird to 0.5.1 as part of the MCX suite v2025.10, with added examples/demo scripts explaining the basics of redbird forward modeling, especially these two new demos
https://github.com/fangq/redbird/blob/master/example/demo_redbird_forward_heterogeneous.m
https://github.com/fangq/redbird/blob/master/example/demo_redbird_forward_layered.m
in one of those comments, a difference between redbird and
MCX/MMC that I want to highlight is the detector reading (detphi)
in redbird is fluence (interior to the domain), while in mmc/mcx,
those were more directly derived from detected photons (escaped
light) as "diffuse reflectance" (dref). the connection between the
two was described in the paper you referenced.
As a matter of fact, my student previously wrote a validation
script in mcxlab to test the Eq 7 in [1], see
https://github.com/fangq/mcx/blob/master/mcxlab/examples/demo_diffuse_reflectance_validation.m
However, in most DOT literature, the measurements used for data
analysis were mostly fluence, instead of dref. This is because in
the diffusion regime, dref and surface fluence differs just by a
scaling factor - you can see our discussion on this scaling factor
in our "replay" paper, Eqs. 14-15
https://opg.optica.org/boe/viewmedia.cfm?uri=boe-9-10-4588&html=true
at the time, we mostly approached this scaling factor empirically, but now with Eq 7 from [1], it should be more clear:
as you can see, the flux term in Eq 7 can be converted to fluence
via the Fix's law, as described in Redbird's manual Eq 2.11, as
the used boundary condition
https://github.com/fangq/redbird/blob/master/doc/Redbird_manual.pdf
replacing Eq 2.11 into Eq. 7 in [1], the entire angular
integration becomes a single scalar.
Because of this scaling relationship, while most instruments (fibers, cameras) actually measure dref, but after data calibration (scaling the raw sensor reading with arbitrary units), the calibrated data can be readily converted to surface fluence, thus matching easily with the forward solutions from most diffusion solvers.
in short, yes, there is a relationship between dref and
surface fluence, but it is a simple linear scaling relationship
(in diffusion regime), and in reality, they are taken care
of/removed as part of the data calibration. As a result, it is
safe (and has been the general practices in DOT) to directly fit
the fluence-based measurement instead of doing the unnecessary
parallel conversions to dref (for both measurement and the
forward model).
Using fluence for MC based DOT/NIRS is also highly advantageous
because fluence data (interior) has significantly lower noise
compared to dref data (few escaped photons). In the newly released
Redbird 0.5.1, rbrunforward() accepts mmclab's cfg as input, and
can produce detphi as interpolated fluence, which is considered
better than using detected photon data for inverse problem.
let me know if this makes sense.
Qianqian
Dear prof Fang,
I am using Redbird to study light propagation in tissues. I am attempting to convert the internal fluence values into external diffuse reflectance using Eq. (7) from Ref. [1]. As I am not very familiar with radiometric analysis, I would appreciate your insights on whether my reasoning is correct.
In this equation, F is the fluence, R_Fres is the Fresnel reflection coefficient for a photon incident at an angle θ relative to the surface normal, D = 1 / [ 3 (µ_a + µ_s')], and dΩ is the solid angle element.
If I understand correctly, the diffuse reflectance corresponds to the integral of the radiance (fluence and flux contributions) over a hemisphere. The flux term is given by the derivative of the fluence along the z-axis. Since the solid angle element is dΩ = sin(θ)dθdφ, I assume the equation can be rewritten as:
Does it make sense?
Thank you so much for your help :)
Best,
Charly
[1] Alwin Kienle and Michael S. Patterson, "Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium," J. Opt. Soc. Am. A 14, 246-254 (1997)
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Charly CAREDDA
[1] Alwin Kienle and Michael S. Patterson, "Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium," J. Opt. Soc. Am. A 14, 246-254 (1997)
Qianqian Fang
just one more clarification regarding your reply below:
there is really just one formula connecting fluence to dref in the diffusion region, i.e. Eq 7 in [1].
Eq 8 in [1] just combine the Fix's law (Eq. 4 in [1], which is
the same, I believe, as Eq 2.39 in redbird's manual, both
originated from Haskell et al 1994 paper).
by the way, flux and dref are not the same - flux is a vector, defined on a surface patch, only denotes the normal-direction component of the dref.
dref, on the other hand, integrates all escaping photons,
regardless their existing angles, and is a scalar.