How to Analog polarization camera?

[wxw19990405]

Summary

The result of the rendered stokes vector is not as expected (there is a rectangle with "linearly polarized" material in front of the camera)

System configuration

System information:

OS: windows 11
Python version: 3.9
Mitsuba version: 3.0
Variants compiled: "llvm_spectral_polarized"

Description

I try to put a polarizer in front of the camera (polarizer is defined by the rectangle of the polarizer through the material) to simulate the polarizer camera. I convert the positions of the polarizer and camera according to my understanding. Because this is the first time I have contact with and learn to apply mitsuba3 rendering, there may be errors in the position transformation. If I understand correctly the polaroid should be 0.5 in front of the camera.

The angle of the polarizer is 0 degree, according to my knowledge, S0 should equal to S1 and S2=0, but the result display S1=0, S2!=0

the code and result are display as following(really need help, thank you very much!)

meshes that i used in the code
meshes.zip

Steps to reproduce

1. sence setting

scene1 = mi.load_dict({
        'type':'scene',
        'bsdf':{
            'type':'pplastic',
            'diffuse_reflectance':{
                'type':'rgb',
                'value':[0.2, 0.25, 0.7],
            },
            'alpha':0.1,
            'id': 'bsdf-measured'
        },
        'intergrator':{
            'type':'stokes',
            'intergrator':{
                'type':'volpath',
                'max_depth':-1
            }
        },
        'sensor':{
            'type':'perspective',
            # 'fov_axis':'larger',
            'focal_length':'12mm',
            'to_world':T.rotate([0,1,0],90).translate([0,0,75]).rotate([0,0,1],90).rotate([0,1,0],180),
            'sampler':{
                'type':'ref',
                'id':"sampler"
            },
            'film':{
                'type':'ref',
                'id':'film'
            }
        },
        'emitter':{
            'type': 'point',
            'id': 'emitter-envmap',
            'intensity': {
                'type': 'spectrum',
                'value': 5000.0,},
            'to_world': T.rotate([0, 0, 1], 10).rotate([0, 1, 0], 90).translate([0,0,74]),
        },
        },
        'shape1': {
            'type': 'ply',
            'filename': "E:/Mitsuba/dragon/meshes/dragon.ply",
            'bsdf': {
                'type': 'ref',
                'id': 'bsdf-measured'
                },
            'to_world':T.translate([0,0,-30]).scale([100,100,100]).rotate([0,0,1],6).rotate([1,0,0],90)
        },
        'shape2': {
            'type': 'rectangle',
            'bsdf': {
                'type': 'polarizer',
                'theta': {
                    'type': 'spectrum',
                    'value': 0
                }
            },
            'to_world':T.rotate([0, 1, 0], 90).translate([0,0,74.5]).rotate([0,0,1],0),
        },
        'shape3':{
            'type':'ply',
            'filename':"E:/Mitsuba/dragon/meshes/plane.ply",
            'to_world': T.translate([0,0,-30]).rotate([1, 0, 0], 90).scale([10,10,10]).rotate([0,0,1],180),
            'bsdf':{
                'type':'diffuse',
                'reflectance':{
                    'type':'ref',
                    'id':'texture-checkerboard'
                }
            }
        },
    })

2. sensor transform
   'to_world':T.rotate([0,1,0],90).translate([0,0,75]).rotate([0,0,1],90).rotate([0,1,0],180),
3. polarizer transform
   'to_world':T.rotate([0, 1, 0], 90).translate([0,0,74.5]).rotate([0,0,1],0),
4. result(from top to end is S0, S1, S2)
   

[wxw19990405]

I discovered another problem while trying to solve the above problem. This time I directly define the Angle of the polarizer instead of the rotation of the rectangle, when the rotation Angle is 45°, then S1 should be equal to 0, but the result is this

the code attachs as following（the configration is same）：

import mitsuba as mi
mi.set_variant("llvm_spectral_polarized")
from mitsuba import ScalarTransform4f as T

scene = mi.load_dict({
        'type':'scene',
        'bsdf': {
            'type': 'pplastic',
            'diffuse_reflectance': {
                'type': 'rgb',
                'value': [0.2, 0.25, 0.7],
            },
        'alpha': 0.1,
        'id': 'bsdf-measured'},
        'intergrator':{
            'type':'stokes',
            'intergrator':{
                'type':'volpath',
                'max_depth':-1

            }
        },
        'sampler':{
            'type':'independent',
            'sample_count':512,
            'id': 'sampler',
        },
        'film':{
            'type':'hdrfilm',
            'width':700,
            'height':700,
            'pixel_format': 'rgb',
            'rfilter':{
                'type':'gaussian'
            },
            'id': 'film'
        },
        'sensor':{
            'type':'perspective',
            'focal_length':'12mm',
            "to_world": T.look_at(
                origin=T.rotate([0, 0, 1], 0).rotate([0, 1, 0], 90) @ mi.ScalarPoint3f([0, 0, 75]),
                target=[0, 0, 0],
                up=[0, 0, 1]),
            'sampler':{
                'type':'ref',
                'id':"sampler"
            },
            'film':{
                'type':'ref',
                'id':'film'
            }
        },
        'emitter':{
            'type': 'constant',
            'radiance': {
                'type': 'spectrum',
                'value': 1,
            }
        },
        'texture':{
            'type': 'checkerboard',
            "color0": 0.06,
            'color1': 0.2,
            'to_uv': T.scale([50, 50, 0]),
            'id': "texture-checkerboard",
        },
        'shape1':{
            'type':'ply',
            'filename':"E:/Mitsuba/dragon/meshes/plane.ply",
            'to_world': T.translate([0, 0, -30]).rotate([1, 0, 0], 90).scale([10,10,10]),
            'bsdf':{
                'type':'diffuse',
                'reflectance':{
                    'type':'ref',
                    'id':'texture-checkerboard'
                }
            }
        },
        'shape2': {
            'type': 'rectangle',
            'bsdf': {
                'type': 'polarizer',
                'theta': {
                    'type': 'spectrum',
                    'value': 45
                }
            },
            'to_world': T.look_at(
                origin=T.rotate([0, 0, 1], 0).rotate([0, 1, 0], 90) @ mi.ScalarPoint3f([0, 0, 74.5]),
                target=[0, 0, 0],
                up = [0,0,1]),
        },
        'shape3': {
            'type': 'ply',
            'filename': "E:/Mitsuba/dragon/meshes/dragon.ply",
            'bsdf': {
                'type': 'ref',
                'id': 'bsdf-measured'
            },
            'to_world': T.translate([0, 0, -30]).scale([100, 100, 100]).rotate([0, 0, 1], 6).rotate([1, 0, 0], 90)
        }
    })
image = mi.render(scene)
bitmap = mi.Bitmap(image, channel_names=['R', 'G', 'B'] + scene.integrator().aov_names())
channels = dict(bitmap.split())
mi.util.write_bitmap("2.png", channels['S1'].convert(srgb_gamma=True))