Using Linear Variable Filters in Spectroscopy Applications

DELTA's linear variable dichroic filter measures 60mm long and has a coated area length of 58.1mm. This article shows how the spectral performance of the linear variable dichroic illustrated by FTLi750c.fsy relies on the width of the light spot (Figure 1) and angular distribution of the light incident on the dichroic filter.

The edge is positioned at 750nm at one end of the dichroic and at 300nm at the other end of it. The light spot is believed to be defined by a rectangular slit 10mms high and centered at 60% of the entire length.

Dependence on the Width of the Light-spot

Predicted transmission of unpolarised and parallel light at AOI = 45 Degrees. Black curve: width = 0.5mm, violet curve: width = 1.0mm, blue curve: width = 1.5mm, green curve: width = 2.0mm, red curve: width = 2.5mm, brown curve: width = 3.0mm.

Figure 1. Predicted transmission of unpolarised and parallel light at AOI = 45 Degrees. Black curve: width = 0.5mm, violet curve: width = 1.0mm, blue curve: width = 1.5mm, green curve: width = 2.0mm, red curve: width = 2.5mm, brown curve: width = 3.0mm.

With increasing width of the light spot, the steepness of the edge decreases slightly. Depending on the exact application, it may be possible to work with a width of a couple of millimeters or more.

Dependence on the Angle of Incidence (AOI)

Transmission curve shifts towards shorter wavelength as AOI increases.

Figure 2. Transmission curve shifts towards shorter wavelength as AOI increases.

The transmission curve moves towards shorter wavelength as the Angle of Incidence (AOI) increases (Figure 2). But the shape of the edge is relatively stable in the angular range examined. AOI gradually increases from 45 – 8 Deg. = 37 Degrees to 45 + 8 Deg. = 53 Degrees in steps of 2 Degrees. The light spot width is kept constant at 1.5mm and the light is believed to be unpolarised.

Dependence on the Opening Angle (OA)

Assuming an even angular energy distribution, in a non-parallel light bundle with an opening angle of OA Degrees, the averaged transmission is predicted to be as shown.

3a

Assuming an even angular energy distribution, in a non-parallel light bundle with an opening angle of OA Degrees, the averaged transmission is predicted to be as shown.

3b

Figures 3a and 3b. Assuming an even angular energy distribution, in a non-parallel light bundle with an opening angle of OA Degrees, the averaged transmission is predicted to be as shown.

Considering a uniform angular energy distribution, in a non-parallel light bundle with an opening angle of OA Degrees, the averaged transmission is predicted to be as shown in Figures 3a and 3b. OA i.e. half cone angle is increasing from 0 Degrees to 8 Degrees in steps of 1 Degree. Steepness of the ensuing edge decreases steadily with increasing OA.

Angling of Linear Variable Filters

It is normal to tilt the filter slightly to prevent inter-reflections between filters placed in series, and also to prevent direct reflection into a laser. Figure 4 displays a characteristic example of the angular dependence of a linear variable edge filter.

LWP720x3 Edge position vs AOI (0 - 30 Deg. Steps = 5 Deg).

Figure 4. LWP720x3 Edge position vs AOI (0 - 30 Deg. Steps = 5 Deg).

In the multi layered coating, the phase thickness of the layers is described by

Where N is the refractive index of the layer, ë is the wavelength of light, D is the physical thickness of the layer, and è is the angle of light propagating in the layer.

According to Snells law, the angle of light in the layer is connected to the angle of incidence in air, V.

Hence

The coating predominantly contains a large number of layers and every second exhibits a higher refractive index than the other. Nevertheless, it is customary to introduce an effective refractive index to represent the entire multilayer

The coating treated (Figure 4) is composed of SiO2 and Ta2O5. At 720nm wavelength, these materials have refractive indices of approximately 2.1085 and 1.4771 rendering an effective refractive index of 1.7648.

Considering a wavelength of 721.5nm at normal incidence (the T=50% point and the black curve), the following values can be calculated for the rest of the angles as illustrated in Figure 4.

  • AOI= 5 Degrees => 720.6nm
  • AOI = 10 Degrees => 718.0nm
  • AOI = 15 Degrees => 713.7nm
  • AOI = 20 Degrees => 707.8nm
  • AOI = 25 Degrees => 700.5nm
  • AOI = 30 Degrees => 691.9nm

The values fit the curves fairly well, but polarisation effects evidently course a harsh distortion of the edge at angles of incidence of over 20 Degrees. It is recommended to keep the angles of incidence less than 15 degrees.

Orientation of DELTA’s Linear Variable Filters

The following paragraphs describe how to orientate DELTA’s linear variable filters (LVFs) to make them perform as well as possible.

Orientation of LVFs with Respect to the Incident Light

Orientation of the filter with respect to the incident light.

Figure 5. Orientation of the filter with respect to the incident light.

The filter substrate features a corner with a facet. It is important to ensure that the light enters the filter from the opposite side as illustrated in Figure 5. Improper mounting of the filter may result in slight leakage of light in the blocking bands. The short wavelength end of the filter is also marked by the facet.

Orientation of LVFs When Used in Series

Orientation of two LVFs when they are placed in series.

Figure 6. Orientation of two LVFs when they are placed in series.

When several LVFs are placed in series either to form a bandpass with an LWP and an SWP or to increase blocking with two similar filters it is important to reduce the inter reflections. This is performed by tilting each filter slightly with regard to the adjoining filters. It is recommended to angle each filter by 1° to 2° in the vertical plan, as shown in Figure 6.

Conclusion

DELTA’s LVFs are especially suited for applications in spectroscopy. The spectral performance of the linear variable dichroic depends on the width of the light spot and angular distribution of the light incident on the dichroic filter. Orientation of DELTA’s LVFs is recommended to make them perform as well as possible.

About DELTA Optical Thin Film

DELTA designs and manufactures high-performance filters for UV- VIS-NIR applications in high volume at attractive prices. Highlights are fluorescence filter sets, dichroic and polarisation beam splitters, and most of all, unique Linear Variable Filters in unrivalled quality.

This information has been sourced, reviewed and adapted from materials provided by DELTA Optical Thin Film.

For more information on this source, please visit DELTA Optical Thin Film.

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