Published data on the performance of optical filters are relatively limited, and most information comes from manufacturer literature. However, studies like those by Blifford, Pelletier, and others provide valuable insights into filter behavior under various conditions.
Key Findings
1. Peak Wavelength Shift with Angle of Incidence:
– Blifford measured sensitivities of filters to tilt and found values for \( P = 1/n^{*2} \) ranging from 0.22 to 0.51, with an average value of 0.35.
– Peak transmittance changes with angle were generally less than 10% for angles between 5°–10°.
– Sideband suppression using absorption filters can affect peak transmittance due to fixed edge wavelengths.
2. Spatial Variations in Performance:
– For a filter with a peak wavelength of 500 nm and approximately 2.1 nm bandwidth, peak transmittance ranged between 54% and 60% across its surface.
– Variations are often caused by water vapor adsorption before a cover slip is applied.
3. Temperature Effects:
– Blifford reported peak wavelength shifts of +0.01 nm/°C to +0.03 nm/°C over a range of −60°C to +60°C.
– Pelletier provided coefficients of optical thickness change for dielectric materials:
– Zinc sulfide: \( (4.8 \pm 1.0) \times 10^{-5} \, ^\circ\text{C}^{-1} \)
– Cryolite: \( (3.1 \pm 0.7) \times 10^{-5} \, ^\circ\text{C}^{-1} \)
– Filters showed hysteresis during initial temperature cycling, particularly when uncemented or heated above 100°C.
4. Advances in Deposition Techniques:
– Takahashi highlighted the superior performance of energetically deposited films, which exhibit lower temperature coefficients compared to thermally evaporated films.
– In energetically deposited filters, the expansion coefficient of the substrate often dominates performance, achieving shifts as low as \( 1 \, \text{pm/°C} \) in communication filters at 1550 nm.
5. Illumination-Induced Changes:
– Title reported permanent shifts in the passband of filters exposed to high-intensity light, attributed to changes in zinc sulfide properties (e.g., transformation to zinc oxide under UV light in the presence of moisture).
6. Infrared Filters:
– Baker and Yen studied angle-of-incidence and temperature effects:
– For angles up to 50°, peak wavelength shifted as expected with no significant bandwidth variation.
– Above 50°, passband shape and peak transmittance deteriorated.
– Temperature coefficients ranged from \( +0.0035\% \, ^\circ\text{C}^{-1} \) to \( +0.0125\% \, ^\circ\text{C}^{-1} \).
– Filters using zinc sulfide and lead telluride exhibited temperature coefficients as low as \( -0.0135\% \, ^\circ\text{C}^{-1} \), with designs achieving zero temperature coefficients using material compensation.
Practical Implications
1. Design Considerations:
– Filters must account for environmental factors like angle of incidence, temperature, and illumination.
– Use of energetically deposited coatings and material combinations can reduce temperature sensitivity and enhance performance.
2. Applications:
– Infrared filters with low or zero temperature coefficients are ideal for radiometric and communication applications.
– Visible and UV filters should consider water adsorption effects and require protective coatings.
3. Future Directions:
– Advanced modeling and deposition techniques will continue to improve filter stability and performance under diverse conditions.
