Many optical filters for use in various applications have problems caused by reflection of the filters themselves.  For example, in some cases, an optical filter for use in an imaging optical system involves a phenomenon that part of light transmitted through the filter is reflected by another member and re-enters the optical filter from a light emitting surface of the optical filter.  In such a case, if the optical filter has a reflectance in a wavelength region of the incident light, the light reflected by another member and re-entered is reflected again by the optical filter.  As a result, a problem caused by the light reflected by the optical filter occurs.  Therefore, further enhancement of the anti-reflection function of the optical filter has been strongly desired. 
A light-absorbing-type optical filter including an absorbent structure, whose surface reflectance is made close to zero as far as possible, can also provide desired transmission characteristics by adjusting light-absorbing characteristics. 
In general, as such an optical filter of the type having absorption in a desired wavelength region, an absorption-type ND (Neutral Density) filter for use in a light diaphragm device is widely known. 
The light diaphragm is provided in an optical device to control the amount of light incident on a solid-state imaging element such as a silver halide film, or CCD and CMOS sensors.  Some light diaphragms are structured so as to be narrowed to be smaller as the object field becomes brighter.  When an object is photographed in the field of high brightness or in good weather, such structured light diaphragm enters a so-called small aperture state, which is susceptible to influence such as a diaphragm hunting phenomenon and a light diffraction phenomenon, which may cause deterioration in image performance. 
As a countermeasure to this, it is devised that an ND filter is arranged near the aperture along an optical path through the diaphragm or an ND filter is directly attached to a diaphragm blade.  The amount of light can be controlled in such an ND filter arrangement to increase the diaphragm aperture even if the object field has the same brightness. 
With recent advances in sensitivity of the imaging element, improvements have been made to further reduce light transmittance by increasing the density of ND filters.  As a result, the diaphragm aperture can be prevented from becoming too small, even if an imaging element with high sensitivity is used. 
A transparent substrate made of glass or plastic material is used for the substrate for making the ND filter.  Regarding the demands for machinability into any shape, reduction in size and weight in recent years, various plastic materials have come to be widely used as the substrate.  Examples of the plastic materials for the substrate can include PET (polyethylene terephthalate), PEN (polyethylene naphthalate), PC (polycarbonate), PO (polyolefin).  Regarding them, in particular, a norbornene-based resin and a polyimide-based resin as represented by Arton (product name, fabricated by JSR Co., Ltd.), Zeonex (product name, fabricated by Nippon Zeon Co., Ltd.) have been preferably used, from a comprehensive point of view including heat resistance and flexibility as well as a cost-related point of view. 
Even in the ND filter, with respect to further high sensitivity, high resolution of the recent solid-state imaging element, there is an increasing possibility that a captured image has a problem such as ghost and flare caused by reflection of the filter itself as described above. 
The following methods have been known for reflection reduction.  First, JP 08-075902A (Patent Literature 1) proposes a method of suppressing the reflectance of any wavelength region, for example, by laminating several types of thin films each having the different refractive indexes and being made of different materials such as SiO2, MgF2, Nb2O5, TiO2, Ta2O5, and ZrO2 to form a multi-layer film-type anti-reflection film.  In addition, JP 2009-122216A (Patent Literature 2) discloses an ND filter using a fine periodic structure as an anti-reflection structure.