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Understanding AOI is an integral part of the filter-purchasing process. For those looking to optimize AOI and cone angle requirements, we suggest you read on - from steering optics to interference filters, this blog addresses the many different influences on AOI that might not be recognizable to the naked eye. Our products ensure you get the best, most refined spectral response possible - but why not learn a bit more about the science behind this phenomenon?

Angle of incidence and cone angle

In optics, all angles are measured with respect to the normal (perpendicular to the surface). This includes the angle of incidence (AOI), angle of reflection and angle of refraction. The AOI is the average angle at which the light hits the surface. If the light beam comes in perpendicular to the surface, the AOI is zero.

Some light beams are collimated, meaning all the light is moving in the same direction These beams are not being focused or defocused. In this case, the cone angle is also zero. The cone angle describes the deviation of the AOI in a converging or diverging beam. It is often expressed as a half cone angle in a tolerance. For instance, a beam with an AOI of zero might have a distribution of angles (cone angle) of + 20 degrees. The cone of light hitting the surface will contain a total of 40 degrees centered around zero.

For steering optics (mirrors and dichroics), this can become more complicated. You may have an example where the AOI is 45 degrees with a ½ cone angle of 10 degrees (or + 10 degrees). The light hitting the surface will contain light at all angles between 35 degrees and 55 degrees. See our AOI tech notefor more information about cone angles and how they relate to f/# and numerical aperture.

Why do AOI and ½ cone angle matter for interference filters?

Interference filters work by layering thin-films of materials with different refractive indices (high and low) in an alternating pattern on a substrate. By keeping the layers and materials constant and only changing the AOI, it can be shown that the wavelength of maximum interference is proportional to the cosine of the AOI. In a bandpass filter, for example, the peak transmission wavelength will decrease as the AOI increases. Remember, cosine of zero degrees (AOI=0) is 1 and cosine of 90 degrees (parallel to the surface, AOI=90) is zero. The greater the AOI, the lower the cosine and the lower the observed wavelength.

Increasing the cone angle causes both a lowering of the center wavelength and a broadening of the spectral response. The beam described by the cone angle contains light at all the intervening wavelengths. So, the response of a 20 degree half cone angle is the response of all angles between 20 and zero added together. Because filter design includes the AOI in its optimization, it is difficult to design a filter that will work well at large cone angles.

Omega Optical has been developing new coating materials to mitigate the effect of angle on the spectral response. We can also help you to optimize the AOI and cone angle requirements for your system. Contact a member of our team today.

Thin film optical filters can reversibly shift off of their nominal wavelength for multiple reasons, the chief among them is angle of incidence, but the second most significant is temperature.  For filters in well controlled temperature environments, like an open air mounting in a laboratory, or filters with wide bandwidths or gentle slopes, the temperature effects on a filter are generally negligible.  However many filters have much higher temperature excursions, such as those used at cryogenic temperatures, or used on automobiles or aircraft, while others have very narrow bandwidths or steep slopes which tend to be more sensitive to temperature. For temperatures below about 125 C, wavelength shifts are fully reversible.

Different material sets, and different deposition methods can lead to very different rates of change with temperature.  This is caused by multiple factors, including the coefficient of expansion (CTE) of the coating materials and the amount of densification the coating receives from temperature and ion assist during deposition.  Above is a fairly standard PARMS (plasma-assisted reactive magnetron sputtered) coating, which has strong plasma assist during deposition and is well densified.  These types of coatings tend to have wavelength shifts with temperature of about 0.007 nm/C in the visible.  Below is a typical protected coating, which is deposited at relatively low temperature and without ion assist.  These type of coatings have wavelength shifts with temperature of 0.014nm/C in the visible.

Different substrates can also affect the temperature dependence of wavelength performance. This is because the temperature shifts have to do with the difference of the CTE of the coating in relation to the substrate.  Even though PARMS coatings already have a very low temperature shift, they can be further reduced by careful choice of substrate. Below are graphs of edge shift versus temperature on two different substrates from the same run. The temperature dependence of the coating varies drastically between them because of the CTE difference in the glass substrates. 

As temperatures get very high, 125-550 C, irreversible annealing shifts occur in the thin-films. Omega recently presented a paper on this at the Optical Interference Conference in Whistler, BC Canada. Contact us to request a copy of this paper when it becomes available. At even higher temperatures (>550 C), phase transitions begin to occur in the films, causing an increase in scatter within the films and a decrease in performance. If you have a very demanding filter, or plan on using your filter in an environment with large temperature excursions, then it is worth discussing this with our sales team so that we can help you get the right filter for your demanding application. 

Contact us to request a copy of the OIC paper

Refractive index is a dimensionless quantity that describes the speed of light in a medium with respect to the speed of light in vacuum. Most materials have a refractive index > 1 which means that light travels slower in a medium than it does in vacuum. The higher the refractive index, the slower the light moves in that medium. When a researcher looks up “the refractive index” of a material in a book, it is often reported as single number, but it’s not that simple.

In reality, refractive index is a complex number comprised of a real part (n) and an imaginary part (k). The real part, as described above, describes the speed of light in the material. The imaginary part of the refractive index is the extinction coefficient in the material - a measure of how much light is being absorbed at a given wavelength. Both n and k are wavelength dependent, so they vary over the spectrum.

The refractive index of a thin film can also vary significantly from that of the bulk material reported in books. The refractive index of a thin-film depends on a myriad of process conditions including deposition rates, gas flow rates, oxidation plasma parameters, base vacuum pressure, etc. Small changes in these parameters can affect the film structure and density which in turn affect the refractive index and the final product.

Interference filters are typically made with materials that do not exhibit absorption (k) in the wavelengths of interest, so that part of the refractive index can be neglected. Interference filters work because of constructive and destructive interference between alternating layers of high refractive index (n) and low refractive index materials. The most basic interference filter is a quarter wave stack. A “quarter wave” occurs when the product of the refractive index and the physical thickness of a layer is equal to ¼ of the wavelength being observed. Thin-film designers refer to this product as the optical thickness. Our thin-film design software calculates the required physical thicknesses of each layer to achieve desired spectral performance, but we often monitor film growth using optical thickness. Needless to say, this would be impossible without having tight control over the refractive index in our layers.

Next time in the blog, find out more about how we measure refractive index and keep our processes running optimally for a consistent product.     

At Omega Optical, we supply a range of precision filters and dichroic mirrors designed exclusively for flow cytometers. In this blog post, we’ll explore the basic working principles of flow cytometry to explain how our optics are increasingly important for high throughput, multiplexed flow cytometry.

Flow Cytometry: Fluidics

All flow cytometers are based on central fluidics systems known as flow cells which contain a continuous liquid stream traveling through the cytometer. Samples in suspension are injected into the center of the sheath fluid as it passes through the nozzle which ‘focuses’ the liquid stream according to the cells’ hydrodynamic radii. This causes them to flow through the system in single file.

At the heart of the flow cytometer is a laser, or multiple lasers, that is/are pointed through the liquid stream. Several different optical detectors obtain the signals generated by light interacting with the flowing cells. These include forward scattered and side scattered light, alongside characteristic fluorescence.

Measuring Scattered Light & Fluorescence

One cell at a time, the sample suspension passes through the laser/s and alters the beam. Scattered light indicates the granularity and size of the cell. Forward-scattered light, sometimes abbreviated to FSC, represents the cell-surface area or overall size. Side-scattered light, or SSC, provides information about the cell’s internal composition and structure. Fluorophores bound to labeled cells will also fluoresce when excited by incoming laser light. Each of these signals is generated simultaneously, providing rich detail about the cellular population, cell size, composition, and structure.

If you would like to learn more about the optimal filter layout, take a look at our flow cytometry application page

Engineers continue to push the boundaries of possibility in flow cytometry through multicolor detection. Fluorophores are sensitive to specific wavelengths of light, emitting characteristic signals when excited by specific wavelengths. For example, dyes based on fluorescein (FITC) have excitation and emission peak wavelengths in the region of 495 and 519 nanometres (nm). Using one laser and a single fluorescent reagent only gives limited insights into the type of cells within a population.

In a multichannel system, cell suspensions are stained with multiple fluorescent dyes and the flow cell is intersected with a sequence of laser beams. Precision optical filters designed to acquire signals of specific spectral bandwidths while avoiding cross-talk between channels are absolutely essential. Further to that, flow cytometry is rapidly moving into the realms of big data, leaving traditional histograms and scatter graphs behind in favor of advanced data analysis and visualization software - though this deserves an article of its own to fully do the subject justice.

Contact us today if you would like to learn more about our range of dichroic filters and mirrors for flow cytometers.

Interference filters are expensive primarily because there are a large number of competing requirements when manufacturing them. Most often, it is not a single parameter that moves the part from one camp to the other but instead a combination of requirements. On their own, these requirements don’t create significant hurdles. In concert, however, these can result in difficult manufacturing processes, low yields, and high prices. There are two areas where challenges can occur, the manufacturing process and the filter’s specification.

1. Making an abrupt transition from deep blocking to high transmission requires hundreds of interfering layers, requiring deposition times on the order of days.

Not only do long coating runs have a higher probability of failure, they also have a high consequence of that failure. Consider the impact of a system issue that aborts a coating 20 hours into the run and then requires new substrates followed by a rerun of the coating.

2. The portion of the coating run that simultaneously meets multiple requirements (transmission, blocking, transition slope, surface, and cosmetic requirements, etc) can be low, reducing the yield and driving up the price.

This is because the coating performance must thread the needle between the blocking and transmission requirements and because every coating deposition shows some level of spectral non-uniformity across the coated surface.

With this in mind, let’s take a look at some of the specifications that can contribute to a high filter price.

1. Surface Quality and Dimension

Since there will always be some level of mechanical imperfections in any coating process, a very tight surface quality specification will disqualify some portion of the coated material. This limitation can be dealt with by coating oversized plates and then avoiding the imperfections when configuring the material down to the final size. These oversized plates can also cause an increased price. If, however, the final size is particularly large, the number of parts that can be cut while avoiding the imperfections can be very low. In the extreme, there may be no parts that can be produced from a plate.

2. Aspect Ratio and Coating Specification

The aspect ratio is the ratio of the longest surface dimension to the thickness. The difficulty in producing a precision substrate increases significantly when the aspect ratio surpasses 6:1. The addition of a thick an optical coating compounds the difficulty. Coating stress will deform a substrate. Thicker coatings inherently introduce more stress. While design steps can be taken to mitigate this stress, it is extremely difficult to eliminate it entirely. If a thick optical coating is applied to a thin substrate, the resulting deformation will be extreme. Deep blocking over an extended range or an abrupt transition from rejection to transmission requires a thick coating. These spectral requirements on a large thin part combined with a stringent flatness requirement will be nearly impossible to achieve.

3. Tight Tolerance

Tight spectral tolerances will limit yield. Something to remember is that in optical coatings everything scales with wavelength. The thin-film design that produces a 10nm wide passband in the mid visible, will give a 30nm wide band in the near IR. Similarly, spectral non-uniformity across a coated surface also scales with wavelength. A well-tuned coating chamber can be expected to yield less than 1% spectral variation across a 200mm plate. In the visible, this amounts to a few Angstroms over a 1" part. Consequently, a spectral tolerance of less than a nanometer on a small part in the visible is tight but achievable. If, however, the part is large or it is at a long wavelength, the difficult tolerance can become unachievable, or at best extremely expensive.

In optical thin films, nearly anything can be accomplished given enough time and money. Given that neither of these is in infinite supply, it’s wise to consider not only the impact of any requirement , but also the interaction between all the requirements.