Detailed explanation of the relationship between filter and incident angle

Filters can be divided into two types: absorption type and interference type.

Absorption filters are colored glass that can absorb specific wavelengths of light. The transmittance of absorption type filters is related to the thickness of the glass substrate. The wavelength and bandwidth of absorption filters are not sensitive to the incident angle of the light source, but as the incident angle changes, the thickness of the glass substrate also increases and the transmittance decreases.

Interference filter is based on the principle of light interference. If the optical path difference of the reflected light from two interfaces is:

Reflected light interference enhancement, the film layer is an anti reflection film;

Reflected light interference is reduced, transmission is enhanced, and the film layer is an anti reflective film.

The working principle of the filter.

In fact, interference type filters are much more complex, consisting of alternating high refractive index and low refractive index thin films stacked together.

Interference filters are very sensitive to angles in practice as different incident angles can cause different optical path differences. In the process of using lenses, there are mainly two angles involved: the incident angle and the half cone angle.

The definitions of the two are:

The incident angle of a light source refers to the angle at which light is incident (the angle between the incident light and the normal of the filter).

The half cone angle of a light source is the angle formed by the focusing or diverging edge rays and the center ray.

Under normal circumstances, the angle at which the excitation filter and emission filter operate is 0+/-5 degrees, and the angle at which the dichroic mirror is used is 45+/-1 degrees. For excitation and emission filters, when the incident angle is too large, the spectral map of the filter will drift towards the short wave direction, and the transition band from the cut-off point to the high transmittance point will also increase, resulting in a decrease in relative peak transmittance and cut-off depth (OD value). For dichroic mirrors, when the incident angle is less than or equal to 45 degrees, the spectrum will drift towards longer wavelengths; When the incident angle is greater than or equal to 45 degrees, the spectrum will drift towards shorter wavelengths. The transition zone will change accordingly with the change of angle.

The reflection coefficients of s and p polarized light at the interface can be expressed as:

Both vary with the angle of incidence. When the incident angle of light is relatively large, there is a significant difference in the reflection coefficient of the filter for s and p polarized light, and the spectra are also different.

Can you briefly explain the changes in spectra of different types of filters with different incident angles of light

1. Bandpass filter

As the incident angle increases, the center wavelength will drift towards shorter wavelengths, and the transition band between the cutoff point and the high transmittance point will also change. The broadband of p-light will become wider, while the broadband of s-light will relatively narrow slightly. The peak transmittance of both s-light and p-light will decrease, but the peak transmittance of s-light will decrease more significantly.

In many optical applications, this drift towards shorter wavelengths can lead to a decrease in excitation efficiency for the excitation filter; For the emission filter, it will lead to a decrease in the cut-off depth (i.e. OD value) of the excitation light.

2. Long pass filter

As the incident angle increases, the 50% cut on of both s-light and p-light will drift towards the short wave direction, but the drift amplitude of p-light will be greater. The spectrum of the filter will become stepped when the incident angle of light is relatively large.

3. Short pass filter

As the incident angle increases, the 50% cut on of both s-light and p-light will drift towards the short wave direction, but in contrast to the long pass filter, the drift amplitude of s-light will be greater. The spectrum of the filter will become stepped when the incident angle of light is relatively large.

4. Long pass dichroic mirror

As the incident angle increases, the 50% cut on of both s-light and p-light will drift towards the short wave direction, but the drift amplitude of p-light will be greater. As the incident angle of light decreases, the 50% cut on of both s-light and p-light will drift towards the long wave direction. The spectrum of the filter will become stepped when the incident angle of light is relatively large.

5. Short pass dichroic mirror

As the incident angle increases, the 50% cut-off of both s-light and p-light will drift towards the short wave direction. In contrast to a high pass dichroic mirror, the s-light will drift more towards the short wave direction. As the incident angle decreases, the 50% cut-off of both s-light and p-light will drift towards the long wave direction. The spectrum of the filter will become stepped when the incident angle of light is relatively large.

The influence of the half cone angle on the filter curve is similar to that of the incident angle. As the half cone angle increases, the curve will also drift towards the short wave direction. When the angle of light is too large, the transition band between the cut-off point and the high transmittance point will also change, and the relative spectrum will undergo certain deformation. The transmittance and cut-off depth (OD value) will also decrease. For some optical applications, such as lenses in vision, which have a certain field of view, conventional filters cannot meet this requirement. Therefore, corresponding solutions can only be considered when designing coating layers.

So the R&D technicians of Ruicheng Optoelectronics remind customers that whether it is testing the filter in practice or determining the indicators when customizing the filter, the two important parameters of incident angle and half cone angle must be taken into account.