When integrating an optical filter into the design of an optical system, it is vital to understand the angle of incidence (AOI) and cone half angle (CHA) requirements on the filters to optimize functionality for a wide variety of life sciences and biomedical research applications. The larger the deviation from the designed AOI, the greater the peak wavelength shift and the overall transmission drop.
Increasing the AOI blue shifts the transmission peak toward shorter wavelengths, while reducing the AOI red shifts the transmission peak toward longer wavelengths. In wavelength-dependent application spaces, such as fluorescence spectroscopy and nuclear magnetic resonance, a misaligned filter with too much red/blue shift would be severely detrimental to experimental results or device readings.The larger the CHA of the incoming light, the greater the loss in peak transmission and the greater the peak broadening, which can allow unwanted wavelengths adjacent to the design wavelength to pass through the filter.
Certain design techniques can be implemented by system developers to decrease a filter’s sensitivity to the effects of AOI and CHA. This article discusses the importance of considering angular effects on filter performance in optical system design, as well as potential mitigation strategies.
Impact of angle of incidence
The AOI is defined as the angle between a collimated beam incident on the optic and the surface normal (perpendicular direction) of the filter’s first surface (Figure 1). Altering the AOI from a filter’s specified nominal value will shift the peak transmission toward shorter wavelengths when increasing AOI, and toward longer wavelengths when decreasing AOI. In a simple case with a 0° AOI, this occurs because the optical path difference between reflections off the first and second surfaces of a coating layer shortens, causing interference to favor shorter wavelengths (Figure 2a and 2b). This shift toward shorter wavelengths is known as a blue shift.
Along with the shift toward shorter wavelengths, increasing AOI typically reduces transmission efficiency, creating a noticeable reduction in overall light throughput. At extreme angles deviating from the specified AOI, the entire spectral shape deforms, and the filter’s ability to perform as specified becomes highly compromised (Figure 2, top). This negatively affects overall system throughput and performance. This deterioration can be mitigated by optimizing the optical coating design (Figure 2, bottom) to block and pass specific wavelengths.
As AOI strays more from its optimal angle, the filter’s spectral profile distorts further and creates sidebands or secondary peaks, which can produce inaccurate measurements. Unwanted wavelengths may be passed and desired ones blocked, which affects data collection and accuracy. Thus, considering the AOI when constructing a system is crucial. In some cases, a custom coating design can help to avoid spectral degradation and provide optimal performance where accuracy is paramount, as in the case of virus detection.
During the COVID-19 pandemic, rapid tests were built using gold nanoparticles (AuNPs). These tests detect viral RNA or proteins using spectral shifts, with a red shift (toward longer wavelengths) occurring when nanoparticles aggregate or when the local refractive index increases due to molecular binding. A blue shift (toward shorter wavelengths) can occur if nanoparticles disperse or if the surrounding medium becomes optically less dense.
A misaligned filter in the spectroscopy device reading the samples could lead to false positives or negatives and propagate public health scares. An understanding of AOI directly aided virus detection in the early stages of the pandemic, when fear and tensions were high.
Typical AOI specifications are 0°, with a ±5° tolerance, but designs can sometimes specify other AOIs. Difficulty arises with use cases requiring larger AOI ranges. Ranges exceeding ±10° require significantly more design effort and thicker coating stacks, and they also lead to increased costs. For example, as shown in Figure 2a, a 1064-nm light source (commonly used for research) at 16° AOI will no longer pass through the filter.
When a large AOI range cannot be avoided, absorptive filters, such as color glass, may be a suitable alternative to filters with optical coatings, as their spectral performance is insensitive to the AOI and CHA of the incoming light. Absorptive filters incorporate dyes to select desired wavelengths, rather than thin-film coatings. However, thin-film interference filters typically have better spectral performance, meaning they offer higher transmission and blocking, and often at more precise wavelengths. The spectral range can be (almost) freely designed for coated filters.
For color glass, the optical absorption properties of dyes or other chemical elements dictate the optical spectra, thus rendering custom options limited. If possible, thin-film interference is preferred for its higher performance and wavelength specificity. Building on the COVID example, a virus detector that needs highly specific blocking/passing regions should opt for thin-film interference. However, if the AOI must be compromised, absorptive filters offer helpful AOI flexibility, such as in common laser beamsplitting setups.
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