I want to get the reflectance of each wavelength on a material surface.

[Bambootree0818]

Hello!

I am currently looking to get the reflectance of a material (such as Principled BRDF) in 10nm intervals from 400nm to 700nm.

The image is like using a spectrophotometer to obtain the spectral spectrum of an object's surface.

Is that possible with mitsuba3?
I looked for an API to do that in the references but could not find it successfully as I am a newbie to mitsuba3.

thank you.

[njroussel]

Hi @Bambootree0818

Yes, this is possible.
See this section of a tutorial on how to evaluate a BSDF for a set of incident & outgoing directions. You'll need to make one small change, which is to specify the wavelengths that you want to evaluate for -- this is not needed in the tutorial because it's using and rgb variant. This can be done by setting si.wavelgenths. Note that a single ray carries 4 wavelgenths in _spectral variants, so evaluation of BSDF.eval() will also process 4 wavelengths per set of directions.

[njroussel]

Does this mean that “BSDF.eval() evaluation also processes 4 wavelengths for one set of directions” as you indicated?

Yes.

You can either index in to your output bsdf.eval(...)[0] and discard the 3 other wavelenghts, since they are indentical. Or you can split you range of wavelengths into chuncks of 4, and pass them 4 at a time like:

N_wavelengths = 20 # multiple of 4
wavelengths = np.arange(400.0, 701.0, N_wavelenghts)  
for i in range(N_wavelenghts)[::4]:
     (...)
     si.wavelengths = [wavelengths[i + 0], 
                       wavelengths[i + 1], 
                       wavelengths[i + 2], 
                       wavelengths[i + 3]]
     value = bsdf.eval(mi.BSDFContext(), si, wo)

[Bambootree0818]

I did not know that I could discard the three wavelengths I obtained. I have made a correction based on the code you suggested. It appears to be working well.

I really appreciate your detailed explanations! @njroussel

However, another question has arisen.
I saw an article about using a BSDF measurement device to measure the BSDF of a real sample and fitting mitsuba3's material to it.
In that case, the function used to evaluate the BSDF of the material prepared by mitsuba3 was also bsdf.eval().

Are the values output in my code this time also BSDF values?

What I want is the reflectance of the material (ratio of reflected light intensity to incident light intensity, range 0~1), which seems different from the BSDF value (0 ~ ∞).

Code

import mitsuba as mi
import numpy as np
import drjit as dr

mi.set_variant('scalar_spectral')

bsdf = mi.load_dict({
    'type': 'principled',
    'base_color': {
            'type': 'rgb',
            'value': [1.0, 0.0008, 0.0095]
    },
    'metallic': 0.3,
    'specular': 0.3,
    'roughness': 0.3,
    'spec_tint': 0.0,
    'anisotropic': 0.0,
    'sheen': 0.0,
    'sheen_tint': 0.0,
    'clearcoat': 0.0,
    'clearcoat_gloss': 0.0,
    'spec_trans': 0.0
})

# Define a range of wavelengths
N_wavelengths = 20
wavelengths = np.arange(400.0, 701.0, N_wavelengths)  

#print(wavelengths)

def sph_to_dir(theta, phi):
    """Map spherical to Euclidean coordinates"""
    st, ct = dr.sincos(theta)
    sp, cp = dr.sincos(phi)
    return mi.Vector3f(cp * st, sp * st, ct)

# Calculate reflectance at each wavelength
reflectance_spectrum = []
for i in range(0, len(wavelengths) - 3, 4):
    # Create a (dummy) surface interaction to use for the evaluation of the BSDF
    si = dr.zeros(mi.SurfaceInteraction3f)

    # Specify an incident direction with 45 degrees elevation
    si.wi = sph_to_dir(0, 0)

    #Define wavelength
    si.wavelengths = [wavelengths[i],
                      wavelengths[i + 1],
                      wavelengths[i + 2],
                      wavelengths[i + 3]]
    
    #print(si.wavelengths)

    wo = sph_to_dir(dr.deg2rad(45.0), 0.0)

    # Evaluate the whole array (18000 directions) at once
    value = bsdf.eval(mi.BSDFContext(), si, wo)
    #print(value)
    reflectance_spectrum.append(value)

# Result
for i in range(0, len(wavelengths), 4):
    wl_slice = wavelengths[i:i+4]  
    refl = reflectance_spectrum[i // 4]  

    print(f"Wavelengths: {wl_slice} nm, Reflectance: {refl}")

Result

Wavelengths: [400. 420. 440. 460.] nm, Reflectance: [0.12188934534788132, 0.011093857698142529, 0.0035530731547623873, 0.002195152919739485]
Wavelengths: [480. 500. 520. 540.] nm, Reflectance: [0.001778108300641179, 0.0016859248280525208, 0.0018263242673128843, 0.0023457196075469255]
Wavelengths: [560. 580. 600. 620.] nm, Reflectance: [0.004119507968425751, 0.016360051929950714, 0.14292317628860474, 0.1637125313282013]
Wavelengths: [640. 660. 680. 700.] nm, Reflectance: [0.16548742353916168, 0.16591322422027588, 0.16606703400611877, 0.16613605618476868]

Reflectance of each wavelength of a red paint sample using a spectrophotometer

[njroussel]

Hi again @Bambootree0818

Are the values output in my code this time also BSDF values?
What I want is the reflectance of the material (ratio of reflected light intensity to incident light intensity, range 0~1), which seems different from the BSDF value (0 ~ ∞).

~Yes~, for an energy conserving BSDF that should be the case. Note that, as mentionned in eval's documentation, the output is already multiplied by the cosine foreshortening term to take into account the projected solid angle of your input directions.

[Bambootree0818]

Hello @njroussel . Sorry for the late reply.

Little by little, I learned more about optics and mitsuba3. Thanks for the detailed explanation.

Thanks to you, I was able to get the reflectance in a specific direction using bsdf.eval().
Sorry to keep repeating this, but there is one more thing I am wondering about.

I have set the material color to be strongly red, like [1.0, 0.0, 0.0], yet the long wavelength portion output by bsdf.eval() is small.
For example

Wavelengths: [640. 660. 680. 700.] nm, Reflectance: [0.1654076874256134, 0.16587819159030914, 0.16604872047901154, 0.1661253422498703]

Could you guess why this is?
I had imagined that if the material was red, the long wavelength band would show large values like 0.7,0.8

I could confirm that bsdf.eval_diffuse_reflectance() can be used to obtain values close to the actual sample measurements, but I could not understand the difference in specifications between it and bsdf.eval(). And I'm not sure if this is even appropriate to reproduce the behavior of a real-world spectrophotometer.

Code

import mitsuba as mi
import numpy as np
import drjit as dr

mi.set_variant('scalar_spectral')

bsdf = mi.load_dict({
    'type': 'principled',
    'base_color': {
            'type': 'srgb',
            'color': [1.0,0.0039,0.0092]
    },
    'metallic': 0.3,
    'specular': 0.3,
    'roughness': 0.3,
    'spec_tint': 0.0,
    'anisotropic': 0.0,
    'sheen': 0.0,
    'sheen_tint': 0.0,
    'clearcoat': 0.0,
    'clearcoat_gloss': 0.0,
    'spec_trans': 0.0
})

# Define a range of wavelengths
N_wavelengths = 20
wavelengths = np.arange(400.0, 701.0, N_wavelengths)  

#print(wavelengths)

def sph_to_dir(theta, phi):
    """Map spherical to Euclidean coordinates"""
    st, ct = dr.sincos(theta)
    sp, cp = dr.sincos(phi)
    return mi.Vector3f(cp * st, sp * st, ct)

# Calculate reflectance at each wavelength
reflectance_spectrum = []
for i in range(0, len(wavelengths) - 3, 4):
    # Create a (dummy) surface interaction to use for the evaluation of the BSDF
    si = dr.zeros(mi.SurfaceInteraction3f)

    # Specify an incident direction with 0 degrees elevation
    si.wi = sph_to_dir(dr.deg2rad(0.0), 0)
    
    #Define wavelength
    si.wavelengths = [wavelengths[i],
                      wavelengths[i + 1],
                      wavelengths[i + 2],
                      wavelengths[i + 3]]
    
    #print(si.wavelengths)

    wo = sph_to_dir(dr.deg2rad(45.0), 0.0)

    value = bsdf.eval(mi.BSDFContext(),si,wo)
    #print(value)
    reflectance_spectrum.append(value)

# display result
for i in range(0, len(wavelengths), 4):
    wl_slice = wavelengths[i:i+4] 
    refl = reflectance_spectrum[i // 4] 

    print(f"Wavelengths: {wl_slice} nm, Reflectance: {refl}")

Result

Wavelengths: [400. 420. 440. 460.] nm, Reflectance: [0.110493503510952, 0.010803439654409885, 0.003702295944094658, 0.00232458533719182]
Wavelengths: [480. 500. 520. 540.] nm, Reflectance: [0.0018935453845188022, 0.001802740152925253, 0.0019635080825537443, 0.0025414787232875824]
Wavelengths: [560. 580. 600. 620.] nm, Reflectance: [0.004503182135522366, 0.017773447558283806, 0.14171378314495087, 0.16346140205860138]
Wavelengths: [640. 660. 680. 700.] nm, Reflectance: [0.1654076874256134, 0.16587819159030914, 0.16604872047901154, 0.1661253422498703]

Reflectance of each wavelength of a red paint sample using a spectrophotometer

[njroussel]

Firstly, this can largely depend on the spectral upsampling scheme used (RGB to spectral conversion). Mitsuba uses the following work: A Low-Dimensional Function Space for Efficient Spectral Upsampling.

Secondly, for the configuration you've sent, an RGB evaluation will return [0.225085, 0.000877831, 0.00207078] which lost most of its red component - this is due to the angles and properties of the material.