Measurement of Bidirectional Transmittance Distribution Function

Significance of the Topic

The bidirectional transmittance distribution function (BTDF) describes how light passes through a material in different directions and is essential for characterizing optical properties in sectors such as remote sensing, computer graphics, solar energy, aerospace, coatings and quality control.

Objectives and Overview of the Study

This application note demonstrates that the Agilent Cary 7000 universal measurement spectrophotometer (UMS) can efficiently and accurately measure BTDF in the visible and near-infrared ranges, offering an automated and user-friendly alternative to custom-built instruments.

Instrumentation Used

• Agilent Cary 7000 UMS equipped with universal measurement accessory
• Quartz tungsten-halogen lamp and deuterium arc lamp light sources
• Double monochromator in out-of-plane Littrow configuration with a 4 nm bandwidth
• Optical chopper for dual-beam photometric modulation
• Universal measurement accessory for precise control of polarization, beam size and cone angle
• Turntable system with 0.02° angular resolution for sample and detector positioning
• Dual-band Si/InGaAs photodetector for UV-Vis-NIR detection
• Agilent Cary WinUV software and automated sequencing script

Methodology

Measurements follow spherical coordinate geometry to define incident and transmitted angles. A script cycles through wavelengths (450–1650 nm), viewing zenith angles (–85° to 85°), and polarization states, recording sample, dark and baseline signals. BTDF is calculated as the ratio of corrected sample signal to incident irradiance normalized by cosine of viewing angle and detector solid angle. Uncertainty components—measurement noise, reproducibility, wavelength accuracy, stray light, detector linearity, spatial uniformity, geometric tolerances and polarization—are quantified to derive combined uncertainties of 1.23–1.51% in the visible range and 1.07% in the NIR range.

Main Results and Discussion

Two reference materials were tested: porous PTFE and fused synthetic silica (HOD-500). Both exhibited near-Lambertian BTDF profiles. Angular measurements at multiple wavelengths showed smooth spectral increases. At θ=25°, PTFE BTDF rose steeply above 650 nm while HOD-500 remained flatter; relative differences reached 10% at 450 nm and 23% at 1650 nm. Comparison with a custom-built instrument revealed that the Cary 7000 UMS delivers acceptable uncertainties with simplified configuration and operation.

Benefits and Practical Applications of the Method

Automation of detector positioning, sample rotation and polarization control streamlines BTDF measurements, enabling routine optical metrology in research, QC, device design, material development and calibration tasks without extensive custom setups.

Future Trends and Potential Applications

Further reducing geometric uncertainties by using micrometer-based sample stages, extending measurements to additional spectral regions, integrating BRDF/BTDF workflows, and applying the method to emerging materials such as nanocomposites and textured surfaces will broaden the utility of the Cary 7000 UMS.

Conclusion

The Agilent Cary 7000 UMS provides precise, repeatable and automated BTDF measurements across visible and NIR wavelengths with combined uncertainties below 1.5%. Its user-friendly software and versatile hardware make it an ideal solution for routine optical characterization in both academic and industrial laboratories.

References

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