In a typical gesture-recognition system, a light source emits near-infrared light towards a user.  A three-dimensional (3D) image sensor detects the emitted light that is reflected by the user to provide a 3D image of the user.  A processing system then analyzes the 3D image to recognize a gesture made by the user. 
An optical filter, more specifically, a bandpass filter, is used to transmit the emitted light to the 3D image sensor, while substantially blocking ambient light.  In other words, the optical filter serves to screen out ambient light.  Therefore, an optical filter having a narrow passband in the near-infrared wavelength range, i.e., 800 nm to 1100 nm, is required.  Furthermore, the optical filter must have a high transmittance level within the passband and a high blocking level outside of the passband. 
Conventionally, the optical filter includes a filter stack and a blocking stack, coated on opposite surfaces of a substrate.  Each of the stacks is formed of high-refractive-index layers and low-refractive-index layers stacked in alternation.  Different oxides are, generally, used for the high-refractive-index layers and the low-refractive-index layers, such as TiO2, Nb2O5, Ta2O5, SiO2, and mixtures thereof.  For example, some conventional optical filters include a TiO2/SiO2 filter stack and a Ta2O5/SiO2 blocking stack, in which the high-refractive index layers are composed of TiO2 or Ta2O5, respectively, and the low-refractive-index layers are composed of SiO2. 
In a first conventional optical filter designed to transmit light in a wavelength range of 829 nm to 859 nm over an incidence angle range of 0° to 30°, the filter stack includes 71 layers, the blocking stack includes 140 layers, and the total coating thickness is about 24 μm.  Transmission spectra 100 and 101 at incidence angles of 0° and 30°, respectively, for this optical filter are plotted in FIG.  1.  In a second conventional optical filter designed to transmit light at a wavelength of 825 nm over an incidence angle range of 0° to 20°, the filter stack includes 43 layers, the blocking stack includes 82 layers, and the total coating thickness is about 14 μm.  Transmission spectra 200 and 201 at incidence angles of 0° and 20°, respectively, for this optical filter are plotted in FIG.  2.  In a third conventional optical filter designed to transmit light in a wavelength range of 845 nm to 865 nm over an incidence angle range of 0° to 24°, the filter stack includes 77 layers, the blocking stack includes 148 layers, and the total coating thickness is about 26 μm.  Transmission spectra 300 and 301 at incidence angles of 0° and 24°, respectively, for this optical filter are plotted in FIG.  3. 
With reference to FIGS.  1-3, the first, second, and third conventional optical filters, generally, have a high transmittance level within the passband and a high blocking level outside of the passband.  However, the center wavelength of the passband undergoes a relatively large shift with change in incidence angle.  Consequently, the passband must be relatively wide to accept light over the required incidence angle range, increasing the amount of ambient light that is transmitted and reducing the signal-to-noise ratio of systems incorporating these conventional optical filters.  Furthermore, the large number of layers in the filter stacks and blocking stacks increases the expense and coating time involved in fabricating these conventional optical filters.  The large total coating thickness also makes these conventional optical filters difficult to pattern, e.g., by photolithography. 
To enhance the performance of the optical filter in the gesture-recognition system, it would be desirable to reduce the number of layers, the total coating thickness, and the center-wavelength shift with change in incidence angle.  One approach is to use a material having a higher refractive index than conventional oxides over the wavelength range of 800 nm to 1100 nm for the high-refractive-index layers.  In addition to a higher refractive index, the material must have also have a low extinction coefficient over the wavelength range of 800 nm to 1100 nm in order to provide a high transmittance level within the passband. 
The use of hydrogenated silicon (Si:H) for high-refractive-index layers in optical filters is disclosed by Lairson, et al.  in an article entitled “Reduced Angle-Shift Infrared Bandpass Filter Coatings” (Proceedings of the SPIE, 2007, Vol.  6545, pp.  65451C-1-65451C-5), and by Gibbons, et al.  in an article entitled “Development and Implementation of a Hydrogenated a-Si Reactive Sputter Deposition Process” (Proceedings of the Annual Technical Conference, Society of Vacuum Coaters, 2007, Vol.  50, pp.  327-330).  Lairson, et al.  disclose a hydrogenated silicon material having a refractive index of 3.2 at a wavelength of 1500 nm and an extinction coefficient of less than 0.001 at wavelengths of greater than 1000 nm.  Gibbons, et al.  disclose a hydrogenated silicon material, produced by alternating current (AC) sputtering, having a refractive index of 3.2 at a wavelength of 830 nm and an extinction coefficient of 0.0005 at a wavelength of 830 nm.  Unfortunately, these hydrogenated silicon materials do not have a suitably low extinction coefficient over the wavelength range of 800 nm to 1100 nm.