Angle-Resolved Scattering (ARS)BSDF (Bidirectional Scattering Distribution Function) Spectral System-Lisen Optics

The measurement platform of the iSpec-BRDF Bidirectional Reflectance/Transmittance Distribution Function Spectral Measurement Instrument is illustrated in the diagram. The entire system comprises an illumination system, a spectral detection system, a measurement mechanical system, and spectral data software processing. During the measurement process, spectral measurement software and measurement mechanical system control software are integrated through interface software. This allows the entire measurement process to be automatically controlled by a computer, making the experimental operation convenient, quick, and time-efficient. The fully automated BRDF spectral data acquisition software collects data in real-time and outputs results.

The LiSen Optics iSpec-BRDF spectral system utilizes a high-precision rotational stage combined with a cantilever beam to perform BRDF measurements. The light source is mounted on the outer cantilever, with a rotation radius of 0.5 meters, enabling a single degree of freedom rotation. It can rotate in the zenith angle direction (0° to 90°) about the cantilever axis. The detector is mounted on the inner cantilever and can rotate in two degrees of freedom: zenith angle direction (0° to 90°) about the cantilever axis and azimuthal direction (0° to 360°) about the central turntable axis. The sample is placed on the central turntable and can rotate in one degree of freedom (0° to 360°) in the illumination azimuth angle. Through control of these four degrees of freedom, which include the illumination and detection zenith angles and the illumination and detection azimuth angles, measurements under all conditions of BRDF are achieved. (Please note that due to mechanical limitations during movement, there may be occlusions between the cantilevers, resulting in invalid data for some angles.)

The measurement platform of the iSpec-BRDF Bidirectional Reflectance/Transmittance Distribution Function Spectral Measurement Instrument is illustrated in the diagram. The entire system comprises an illumination system, a spectral detection system, a measurement mechanical system, and spectral data software processing. During the measurement process, spectral measurement software and measurement mechanical system control software are integrated through interface software. This allows the entire measurement process to be automatically controlled by a computer, making the experimental operation convenient, quick, and time-efficient. The fully automated BRDF spectral data acquisition software collects data in real-time and outputs results.

The LiSen Optics iSpec-BRDF spectral system utilizes a high-precision rotational stage combined with a cantilever beam to perform BRDF measurements. The light source is mounted on the outer cantilever, with a rotation radius of 0.5 meters, enabling a single degree of freedom rotation. It can rotate in the zenith angle direction (0° to 90°) about the cantilever axis. The detector is mounted on the inner cantilever and can rotate in two degrees of freedom: zenith angle direction (0° to 90°) about the cantilever axis and azimuthal direction (0° to 360°) about the central turntable axis. The sample is placed on the central turntable and can rotate in one degree of freedom (0° to 360°) in the illumination azimuth angle. Through control of these four degrees of freedom, which include the illumination and detection zenith angles and the illumination and detection azimuth angles, measurements under all conditions of BRDF are achieved. (Please note that due to mechanical limitations during movement, there may be occlusions between the cantilevers, resulting in invalid data for some angles.)

Measurement Principle

The Bidirectional Reflectance Distribution Function represents the reflectance characteristics of an object's surface under different incidence angles at any observation angle, as shown in Figure 1. The bidirectional reflectance distribution function is the ratio of light radiation's reflective luminance to the incident irradiance. Its mathematical expression is:


Figure 1: Light Reflection Geometry Diagram	Figure 2: Light Transmission Geometry Diagram

θ_i,φ_i are the incidence angles and azimuthal angles of the incident light, respectively. θr,φr are are the reflectance angles and azimuthal angles of the reflected light, respectively. Lr is the luminance of the light reflected in direction (θ_r,φ_r) after irradiating the differential element, with a unit of W/㎡·sr·μm, Ei, is the irradiance produced by incident light in the direction(θ_i, φ_i)on the surface, with a unit of W/㎡·μm.Thus, the unit of BRDF is sr^-1。The physical significance of BRDF is the ratio of the luminance emitted in the(θ_r,φ_r )direction to the irradiance produced by incident light from direction(θ_i, φ_i) on the measured surface. The bidirectional reflectance distribution function is a function of incident angle(θ_i, φ_i)、reflection angle(θ_r,φ_r )、and wavelength λ ’s Function.

Measurement Principle

The Bidirectional Reflectance Distribution Function represents the reflectance characteristics of an object's surface under different incidence angles at any observation angle, as shown in Figure 1. The bidirectional reflectance distribution function is the ratio of light radiation's reflective luminance to the incident irradiance. Its mathematical expression is:


Figure 1: Light Reflection Geometry Diagram	Figure 2: Light Transmission Geometry Diagram

θ_i,φ_i are the incidence angles and azimuthal angles of the incident light, respectively. θr,φr are are the reflectance angles and azimuthal angles of the reflected light, respectively. Lr is the luminance of the light reflected in direction (θ_r,φ_r) after irradiating the differential element, with a unit of W/㎡·sr·μm, Ei, is the irradiance produced by incident light in the direction(θ_i, φ_i)on the surface, with a unit of W/㎡·μm.Thus, the unit of BRDF is sr^-1。The physical significance of BRDF is the ratio of the luminance emitted in the(θ_r,φ_r )direction to the irradiance produced by incident light from direction(θ_i, φ_i) on the measured surface. The bidirectional reflectance distribution function is a function of incident angle(θ_i, φ_i)、reflection angle(θ_r,φ_r )、and wavelength λ ’s Function.

Bidirectional Transmittance Distribution Function (BTDF)

The Bidirectional Transmittance Distribution Function represents the transmittance characteristics of an object's surface under different incidence angles at any observation angle, as shown in Figure 2. The bidirectional transmittance distribution function is the ratio of light radiation's transmitted luminance to the incident irradiance. Its mathematical expression is:

Bidirectional Transmittance Distribution Function (BTDF)

The Bidirectional Transmittance Distribution Function represents the transmittance characteristics of an object's surface under different incidence angles at any observation angle, as shown in Figure 2. The bidirectional transmittance distribution function is the ratio of light radiation's transmitted luminance to the incident irradiance. Its mathematical expression is:

Main Technical Features

● The entire system employs a four-axis concentric design, with a simple and stable structure. The rotational stage has a high angular resolution of 0.05° and a high positioning accuracy of 0.10°.

● The entire system is treated with low reflectance matte black, reducing the impact of stray reflections.

● The spectrometer can be configured with different grades (cooling or non-cooling options) and covers a spectral range of 380-1100nm/380-1700nm/380-2500nm.

● The light source can be chosen from a 150W high-power halogen lamp or a super-continuous laser white light source.

● Laser marking indicates the sample's test surface, ensuring coaxial alignment.

● BRDF four degrees of freedom are automatically set and controlled by software across the full range of angles.

● The BRDF fully automated spectral measurement software can be customized based on customer requirements for measurement schemes.

Technical Indicators

Model	iSpec-BRDF-HS400/iSpec-BRDF-UVIR-1.7TEC/iSpec-BRDF-UVIR-2.5TEC
Measurement Spectral Parameters	Spectral Range	iSpec-BRDF-HS400:380~1100nm
		iSpec-BRDF-UVIR-1.7TEC:380~1700nm
		iSpec-BRDF-UVIR-2.5TEC:380~2500nm
	Spectral Resolution	Visible light channel: 1nm
		Near-infrared channel: 10nm
Illumination Source Adjustment	Illumination Range	Automatically adjustable: Zenith angle (θ) = [0°, 90°], Azimuth angle (φ) = [0°, 360°]
	Angular Resolution	±0.05°
	Positioning Accuracy	±0.10°
Illumination Source	Spectral Range of Light Source	350~2500nm/200-2500nm
	Spectral Resolution	Wide spectral output, configurable with filters
	Illumination Source	150W Halogen Lamp/Halogen Plasma White Light Source
	Size of the illuminated area on the object	20mm diameter (vertical incidence), elliptical for oblique incidence
Reflection Observation Adjustment	Observation Range: Automatically adjustable	Zenith angle (θ) = [-90°, 90°], Azimuth angle (φ) = [0°, 180°];
		Zenith angle (θ) = [0°, 90°], Azimuth angle (φ) = [0°, 360°]
	Angular Resolution	±0.05°
	Positioning Accuracy	±0.1°
	Occlusion Angle	±5°(when illumination zenith angle is the same as observation zenith angle)
Transmittance Observation Adjustment (optional)	Observation Range	Automatically adjustable: Zenith angle (θ) = [30°, 90°], Azimuth angle (φ) = [0°, 360°]
	Angular Resolution	±0.05°
	Positioning Accuracy	±0.1°
Spectrometer	Spectral Range	350~1100nm /350~1700nm /350~2500nm
	Detector	2048-pixel BT-CCD/256-pixel InGaAs
	Detector Cooling	Non-cooling/Thermoelectric cooling (optional)
	Integration Exposure Time	1ms-60s
	Spectral Wavelength Resolution	1nm@350~1100nm
		1.5nm@1000~1700nm
		3nm@1000~2500nm
Five-Dimensional Sample Support Platform	Sample XYZαβ bracket, maximum clamping size of 200mm
	Angle adjustment: 360° coarse adjustment, ±5° fine adjustment
	XY Range: 0-6.5mm, Z Range: 0-10mm
	Travel accuracy: 0.02mm-0.04mm
Standard Panel	Diffuse reflectance standard Panel: Diameter 100mm, Reflectance: ≥98% (standard)
	Specular reflectance standard Panel: ≥75mm, Reflectance: ≥95% (optional)
LiSpecView-BRDF Software Features	Software functions include motion platform parameter settings, spectrometer acquisition control, automatic BRDF data measurement based on preset conditions, data acquisition and storage, real-time display of sample photos, 2D spectral display, 3D light intensity distribution.
	The software allows for active control of the robotic arm's zero setting, disabling automatic zero setting of the robotic arm, customizing the detection zenith angle range (0°90° or -90°90°), and loading previously saved standard reference data.

Technical Indicators

Name	Quantity
Five-Dimensional Motion Bracket	1 set
Five-Dimensional Motion Bracket Controller	1 unit
Spectrometer	1 unit
150W Halogen Lamp Light Source	1 unit
Diffuse Reflectance Standard Plate	1 piece
Digital Height Gauge	1 unit
Fiber Optic Cable	1 piece
Collimating Lens	2 pieces
Industrial Camera	1 unit
USB Data Cable	1 piece
Motor Control Cable	4 pieces
Standard Reference White Plate Support	1 piece
Five-Dimensional Sample Bracket	1 piece
Power Cables	2 pieces
Laser Line Angle Measuring Instrument	1 unit
Dark Box	1 piece
Notebook Computer	1 unit
Supporting Software	1 unit

Main Technical Features

● The entire system employs a four-axis concentric design, with a simple and stable structure. The rotational stage has a high angular resolution of 0.05° and a high positioning accuracy of 0.10°.

● The entire system is treated with low reflectance matte black, reducing the impact of stray reflections.

● The spectrometer can be configured with different grades (cooling or non-cooling options) and covers a spectral range of 380-1100nm/380-1700nm/380-2500nm.

● The light source can be chosen from a 150W high-power halogen lamp or a super-continuous laser white light source.

● Laser marking indicates the sample's test surface, ensuring coaxial alignment.

● BRDF four degrees of freedom are automatically set and controlled by software across the full range of angles.

● The BRDF fully automated spectral measurement software can be customized based on customer requirements for measurement schemes.

Technical Indicators

Model	iSpec-BRDF-HS400/iSpec-BRDF-UVIR-1.7TEC/iSpec-BRDF-UVIR-2.5TEC
Measurement Spectral Parameters	Spectral Range	iSpec-BRDF-HS400:380~1100nm
		iSpec-BRDF-UVIR-1.7TEC:380~1700nm
		iSpec-BRDF-UVIR-2.5TEC:380~2500nm
	Spectral Resolution	Visible light channel: 1nm
		Near-infrared channel: 10nm
Illumination Source Adjustment	Illumination Range	Automatically adjustable: Zenith angle (θ) = [0°, 90°], Azimuth angle (φ) = [0°, 360°]
	Angular Resolution	±0.05°
	Positioning Accuracy	±0.10°
Illumination Source	Spectral Range of Light Source	350~2500nm/200-2500nm
	Spectral Resolution	Wide spectral output, configurable with filters
	Illumination Source	150W Halogen Lamp/Halogen Plasma White Light Source
	Size of the illuminated area on the object	20mm diameter (vertical incidence), elliptical for oblique incidence
Reflection Observation Adjustment	Observation Range: Automatically adjustable	Zenith angle (θ) = [-90°, 90°], Azimuth angle (φ) = [0°, 180°];
		Zenith angle (θ) = [0°, 90°], Azimuth angle (φ) = [0°, 360°]
	Angular Resolution	±0.05°
	Positioning Accuracy	±0.1°
	Occlusion Angle	±5°(when illumination zenith angle is the same as observation zenith angle)
Transmittance Observation Adjustment (optional)	Observation Range	Automatically adjustable: Zenith angle (θ) = [30°, 90°], Azimuth angle (φ) = [0°, 360°]
	Angular Resolution	±0.05°
	Positioning Accuracy	±0.1°
Spectrometer	Spectral Range	350~1100nm /350~1700nm /350~2500nm
	Detector	2048-pixel BT-CCD/256-pixel InGaAs
	Detector Cooling	Non-cooling/Thermoelectric cooling (optional)
	Integration Exposure Time	1ms-60s
	Spectral Wavelength Resolution	1nm@350~1100nm
		1.5nm@1000~1700nm
		3nm@1000~2500nm
Five-Dimensional Sample Support Platform	Sample XYZαβ bracket, maximum clamping size of 200mm
	Angle adjustment: 360° coarse adjustment, ±5° fine adjustment
	XY Range: 0-6.5mm, Z Range: 0-10mm
	Travel accuracy: 0.02mm-0.04mm
Standard Panel	Diffuse reflectance standard Panel: Diameter 100mm, Reflectance: ≥98% (standard)
	Specular reflectance standard Panel: ≥75mm, Reflectance: ≥95% (optional)
LiSpecView-BRDF Software Features	Software functions include motion platform parameter settings, spectrometer acquisition control, automatic BRDF data measurement based on preset conditions, data acquisition and storage, real-time display of sample photos, 2D spectral display, 3D light intensity distribution.
	The software allows for active control of the robotic arm's zero setting, disabling automatic zero setting of the robotic arm, customizing the detection zenith angle range (0°90° or -90°90°), and loading previously saved standard reference data.

Technical Indicators

Name	Quantity
Five-Dimensional Motion Bracket	1 set
Five-Dimensional Motion Bracket Controller	1 unit
Spectrometer	1 unit
150W Halogen Lamp Light Source	1 unit
Diffuse Reflectance Standard Plate	1 piece
Digital Height Gauge	1 unit
Fiber Optic Cable	1 piece
Collimating Lens	2 pieces
Industrial Camera	1 unit
USB Data Cable	1 piece
Motor Control Cable	4 pieces
Standard Reference White Plate Support	1 piece
Five-Dimensional Sample Bracket	1 piece
Power Cables	2 pieces
Laser Line Angle Measuring Instrument	1 unit
Dark Box	1 piece
Notebook Computer	1 unit
Supporting Software	1 unit

Angle-Resolved Scattering (ARS)BSDF (Bidirectional Scattering Distribution Function) Spectral System

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