Reflective neutral density filters
Filters are capable of selectively transmitting a portion of the spectrum and rejecting the rest, and are commonly used in spectroscopy, machine vision, and other fields.
1. Interference cut-off filter
Interference cut-off filters refer to high light reflection that allows a certain wavelength range to be highly transmitted away from this wavelength region. The cut-off filter that suppresses the short wave region and transmits the long wave region is called the long wave pass filter, and its characteristic curve is shown in Fig. 1. The cut-off filter that suppresses the long wave region and the transmitted short wave region is called the shortwave pass filter, and its characteristic curve is shown in Fig. 2.
Fig. 1 Characteristic curves of long-wave pass filters Fig. 2 Characteristic curves of shortwave pass filters
2. Bandpass filter
Ideally, the filter has a transmittance of 100% within the passband, which can be described by the bandwidth of the transmitted region and the center wavelength within the passband, as shown in Figure 3(a); However, the actual bandpass filter has an ideal square band and requires more parameters to describe its characteristics, as shown in Fig. 4(b).
(a) Bandpass filter transmittance ideal waveform (b) Bandpass filter transmittance actual waveform
Fig.3 Curve of the transmittance of bandpass filter with wavelength
According to spectral characteristics, bandpass filters are broadly divided into broadband filters and narrowband filters. Filters with a relative half-width of not less than 20% are usually called broadband filters, and filters with a relative half-width of less than 5% are called narrowband filters.
3. Common terms
1. Transmittance (Transmission, T)
The ratio of light flux or light intensity from the transmission of an object is expressed as a percentage (%).
2. Optical density (OD)
Represents the attenuation factor provided by the filter, which is the degree to which the optical power of the incident light is attenuated. Optical density (OD) has the following relationship with transmittance (T):
where T is a value between 0 and 1. When choosing a neutral density filter with a higher optical density, the transmittance of the incident light is lower, that is, the reflectivity is higher. Therefore, when higher transmittance and lower reflectance are required, a neutral density filter with lower optical density should be selected. For example, a filter with an optical density OD of 1 with a transmittance T of 0.1 means that the filter attenuates the beam to 10% of the incident light power.
In addition, there is a linear relationship between the OD value of optical density and the angle θ: OD = kθ
where the k value depends on the optical density range of the neutral density filter.
3. Attenuation (A)
The decibel (dB) representation of spectral transmittance, which is used to characterize the attenuation capacity of an object to the amount of light, is expressed by A. The following relationship exists between attenuation A and transmittance T:
he following relationship exists between attenuation A and optical density OD:
For example, if the attenuation A is 10dB, the optical density OD is 1 and the transmittance is 0.1, which means that the filter attenuates the beam to 10% of the incident light power.
| Transmittance | OD | dB |
| 79% | 0.1 | 1 |
| 63% | 0.2 | 2 |
| 50% | 0.3 | 3 |
| 40% | 0.4 | 4 |
| 30% | 0.5 | 5 |
| 25% | 0.6 | 6 |
| 20% | 0.7 | 7 |
| 16% | 0.8 | 8 |
| 10% | 1 | 10 |
| 5% | 1.3 | 13 |
| 1% | 2 | 20 |
| 0.1% | 3 | 30 |
| 0.01% | 4 | 40 |
| 0.001% | 5 | 50 |
| 0.0001% | 6 | 60 |
Table 1 Relationship between transmittance T, optical density OD and attenuation A
4. Central wavelength (CWL): the wavelength at the center of the passband, the center wavelength of the narrowband filter is generally the working wavelength of the instrument or equipment, and the traditional coating filter often reaches the maximum transmittance near the center wavelength. As shown in Figure 3, λ₀ is the center wavelength.
5. Bandwidth: The spectrum passes through a specific part of the filter light sheet through incident energy. As shown in Figure 3, ∆λ is the width of the passband.
6. Full Width at Half Maxima (FWHM): the difference between the two wavelengths corresponding to half the peak transmittance. As shown in Figure 3, ∆λ₀.₅ is the half-width of the throughband.
7. Relative half-width: the ratio of the half-width of the passband to the central wavelength, expressed as ∆λ₀.₅/λ₀.
8. Blocking range: the wavelength interval of the energy spectral region attenuated by the filter, as shown in Figure 4.
Figure 4 Cut-off range description