Budgeting is a huge part of everyday life. This can be budgeting time or finances between competing priorities, from family, work, and self-care, to food, shelter, clothing, and health, but budgeting also affects enrichment activities such as entertainment, hobbies, and travel. Trade-offs between “need to have” and “nice to have” priorities are in constant competition, and these trade-offs can even happen among elements in the “need to have” group.
The same budgeting exercises are needed when specifying optical filters. Again, trade-offs are commonplace between specific optical performance specifications and costs, and the conditions of use that determine these specifications.
A potential primary user-influenced consideration in the majority of wavelength-selective (band pass (BPF) or edge pass (LPF or SPF and notch) optical filters is the permitted spectral transition zone between high transmission wavelengths and high blocking or reflecting spectral bands that are defined by the particular device’s requirements.
Specifying this transition zone or “dead band” significantly influences the complexity and cost of the majority of optical filters, as it directly limits the required steepness of the filter. In other applications, this can be called band spacing, channel spacing, or isolation bandwidth, among other terms. This spectral separation defines the total budget that is available to “spend” on the influences due to the application and those due to realities associated with filter manufacture.
There are many critical applications and parameters in the manufacturing of filters that influence the spectral width of dead bands. This article discusses these parameters and how they impact the wavelength budget of optical filters.
Application Influences On Wavelength Budget
There are several primary, application-related “consumers” of the available wavelength budget. These are parameters that the application designer control. Filter designers are only able to indicate the impact of these particular parameters and do not have many opportunities to reduce or optimize for these effects.
These effects include:
Operating Temperature Range
All-optical thin-film filters will experience a shift in spectral performance as a function of the operating temperature. With increasing temperature, the majority of filters will shift to longer wavelengths, although some mid‐wave infrared (MWIR) filters make use of materials that act oppositely: they shift to shorter wavelengths with as temperature increases.
However, the direction in which the filter shifts in relation to temperature is not important. What is of chief concern is the total temperature range over which the filter needs to operate.
A design can be targeted to operate at any given temperature, although it is still necessary to factor the shift into the design and characterization, particularly if the filter operates at a different temperature than the test conditions.
The thermally influenced wavelength drift (ΔWLTemp) of a filter is normally specified in terms of the temperature coefficient (Tc in units of pm/C), with typical values falling between 12 pm/C up to 10‐20 pm/C, depending on the substrates and the coating materials multiplied by the temperature range of operation.
ΔWLTemp = Tc x (Max Temp – Min temp)
For example, a filter with a 10 pm/C thermal drift that needs to operate from ‐20 C to 80 C will go through 1 nm of thermal drift from the thermal extremes (10 pm/C x 100 C = 1000 pm (or 1 nm)). It is necessary to subtract this value from the budget set out by the required band spacing.
Operating Angle of Incidence and Angle Range
Multilayer thin-film optical filters will demonstrate a “blue shift” to shorter wavelengths with increasing angle of incidence. Akin to the temperature range detailed above, the nominal angle at which a filter needs to be operational can be accounted for “by design”, and should be factored into characterization.
The range of angles over which the filter needs to meet all the optical specifications is important in terms of wavelength budget. This range of angles can be due to uncertainty, which is generally referred to as the angular tolerance, in the nominal angle of incidence (AOI). It can also be caused by a variation in the angle on the filter due to a focused or divergent (not collimated) incident beam, which is usually specified as the cone half‐angle (CHA).
However, this shift with angle is non‐linear. As a result, a filter with a nominal AOI of 0 deg and a total angular contribution of +/‐ 5 degrees will show a much smaller spectral shift when compared with a filter with a nominal AOI of 45 degrees and a total angular contribution of +/‐5 degrees. Operating at a smaller nominal AOI is recommended where feasible to reduce the impact on the budget.
The actual value of spectral shift is highly dependent on the nature of the design, and as such, it is not possible to provide a typical scale of shift with AOI. To a certain extent, designs can be adjusted to minimize spectral shifts. Alternative material sets can also be chosen, but freedom in design is limited when adjusting this parameter.
The polarization states of the light used in an application can also affect the wavelength budget. Again, the actual polarization state used (s or p polarization) is not important. However, the need for the filter to work for a single polarization state over both polarization states, which is typically referred to as random polarization, meaning it must be fully functional for s and p, is key. Also, the key to this is the average polarization, meaning it must work when the average of s and p polarization is considered. It is important to note that while this is often used in definitions, it is not a valid description of conditions in real-world use.
A filter specified for use at a single polarization (or for use at or near 0 degrees where s and p align) will not have contributed to the wavelength budget from polarization. Conversely, a filter designed to work at a large AOI, or a filter designed to operate over a large angle range for both polarizations, will have to include a large wavelength budget contribution to account for the differences in spectral shape for each polarization at different AOI values.
If uncertain, it is best to assume the filter needs to work for random polarization. Any other case will need explicit control of the polarization of the incident beam, which is generally only seen in laser clean‐up filters.
Variation in the Source and Laser Wavelength
The source wavelength of incident light used in any optical system will vary. The variation may be relatively small and may even be ignored, for instance, in the case of sub GHz variations between HeNe lasers. However, it can also be relatively large, for example, as much as +/‐0.1% for some solid-state lasers.
In some instances, each laser is stable, but there is a device-to-device variation, meaning there is still uncertainty concerning the wavelength the filter will see during use. The result of this is that the dead band in a system that requires the filtering of two different nominal wavelengths will need to be adjusted to take this uncertainty into account, which reduces the total available wavelength budget.
The Effect of Filter Manufacturing on Wavelength Budget
Beyond the requirements of the filter in its specific application, there are many aspects in the actual manufacture of the filters that also need to be considered in terms of wavelength budget.
Almost any filter shape can be designed. However, in practice, manufacturing variations of “real-world” production are critical. Filters have to be designed with factors such as which coating materials are available and considered reliable and the minimization of complexity and thickness are taken into account.
Coatings with increased thickness can negatively influence cost, as well as other parameters such as wavefront error and surface quality. In practice, there is a maximum value to the achievable design edge steepness. As a result, the slope of this edge will always take up a portion of the total wavelength budget.
Once the filter has been designed, it needs to be manufactured. During the manufacturing process, it is extremely unlikely that the edges of the spectral curve will exactly match that specified in the design.
It is necessary to estimate this wavelength targeting offset when a quote is being drawn up and budgeting for it spectrally. The wavelength targeting budget can be minimized to a certain extent if the filter can be actively angle-tuned in application, for instance, tilt-tuned to match the ideal spectral edge position, or by reducing the assumed run success rate. This is assuming that with multiple attempts, the edges will eventually line up with design. However, this is a costly method of reducing the wavelength targeting budget.
Particularly for parts that are larger than a few millimeters, spatial variations in spectral performance due to coating non‐uniformities must also be considered in the wavelength budget. Similar to wavelength targeting detailed below, non‐uniformity is manifested as an offset in the spectral edge position when compared to the design. The main difference is that this offset can be different at different positions on the part to the geometry of the coating approach used.
The total expected uniformity variation, the variation in the edge wavelength, has to be subtracted from the total allowed wavelength budget. It is possible to reduce this by coating configuration, but it can often require set‐up runs. This is also a particularly expensive approach, which runs the risk of quickly producing into diminishing returns, in particular for larger (50 mm) parts. The non‐uniformity is highly design-dependent in addition to these issues, so what is considered a large part from a uniformity perspective will entirely depend on the spectral performance being targeted.
Calculating Wavelength Budget
The following, hypothetical example illustrates the various consumers of wavelength budget discussed above and how this can result in a filter that is not possible to make as specified.
The values below are not representative of a real system, especially the manufacturing margins. As such, these values are provided for illustrative purposes only and are not to be used in the design of an optical system or for specifying filter requirements.
- Spectral transition zone
- Allowed dead band (transition from T>95% to R>98%): 1560 nm to 1545 nm → 15 nm
- This sets the total wavelength budget available
- Operating temperature range
- Tc ~20 pm/C, temperature range ‐40 C to 80 C
- Wavelength shift over temperature range: ~2.4 nm
- Operating AOI range
- AOI range from 20 deg to 25 deg (ie 22.5 +/‐2.5 deg):
- Wavelength shift over AOI range: ~11 nm
- Single polarization
- Wavelength shift to account for polarization: 0 nm
- Source variation
- Variation due to uncertainty in the two sources: ~0.2nm
- Filter design
- Design curve slope from T>95% to R>98%: ~3.0 nm
- Wavelength targeting
- Manufacturing margin for wavelength targeting: ~0.2 nm
- Coating non‐uniformity
- Manufacturing margin for uniformity: ~1.5 nm
Sum of the wavelength budget consumers that are influenced by application:
Temp range (2) + AOI range (3) + Polarization (4) + Source (5) = 2.4 + 11 + 0 = 0.2 = ~13.6 nm
Sum of the wavelength budget consumers influenced by filter manufacturing:
Design (6) + Targeting (7) + Non‐uniformity (8) = 3.0 + 0.2 + 1.5 = ~4.7 nm
Total wavelength budget required: 13.4 + 4.7 = ~18.3 nm
Total budget available (1): 15 nm
As the wavelength budget required by the application and filter manufacturing considerations exceeds by more than 3 nm, it is not possible to manufacture this filter according to the budget available from the targeted dead‐band.
To create a solution that can be manufactured, application trade‐offs would be necessary. These could include reducing the AOI range or nominal AOI, or moving the defined transmission and reflection wavelength points further apart.
The filter manufacturer could also attempt to reduce some of the manufacturing margins, although these are already small contributions to the budget, so the benefits of undertaking this are small. Any gains achieved with this method would need to come with higher costs, because of the higher complexity in the manufacturing process, and the risk of needing to repeat runs.
The two optical system design parameters that can be adjusted most frequently to achieve the most significant benefit in reducing the wavelength shift within the filter dead‐band are:
- AOI and AOI range:
This physical parameter can be modified at the time when the system is designed. It can often have the largest impact on wavelength budget, by reducing the nominal working AOI or by locating the filter in a more collimated part of the beam.
- Filter useable aperture dimensions:
The coating non‐uniformity specification is a function of the spatial area over which the spectral performance must be maintained. By reducing the size of the filter or only specifying the performance over the beam area within a larger physical size, it is possible to minimize the functional effect of non‐uniformity. Specifying performance where it is not functionally needed causes unnecessary increases in complexity and costs.
As is the case in everyday life, filter designers need to set out and live within particular budgets when designing and manufacturing filters. It is most beneficial to engage with the filter design and manufacturing team as early as possible in the system design process to ensure that system design constraints are compatible with filters that can be manufactured in practice.
This information has been sourced, reviewed and adapted from materials provided by Iridian Spectral Technologies.
For more information on this source, please visit Iridian Spectral Technologies.