Perfecting Your Light ®


Bullseye® Apodizing Filters

Bullseye apodizing filterBullseye® Apodizing filters are customizable density gradient filters that change radially from the center to the outside of the optical component. These apodization filters are used to eliminate undesirable intensity variations in optical systems or to modify the wavefront of an optical source.

Bullseye® filters come in two configurations, normal and inverse apodizing:



The normal Bullseye® apodizing configuration decreases in density radially from a dark center, where light is usually at its peak intensity, to the outside edge, where it can become completely transparent. Normal apodizing filters are used to modify a Gaussian light source into a 'top-hat' type of output with a flat wavefront, as can be seen in the animation below.  Standard filters, depending on the product selected, start with a central density between OD1 and OD5 and change to fully transparent as you move to the outer edges of the optical component.  Custom gradients can also be defined.



In the Bullseye® inverse apodizing configuration, the density increases from the center to the outside edge.  Following a Gaussian distribution from a clear center, the outer edges of the optic will achieve a density of OD1 to OD5, depending on the product selected.  These filters are used to create a well-defined Gaussian wavefront, as seen in the animation below, or can be used to eliminate unwanted intensity variations in an optical system.  Custom gradient functions can be defined.




Using a proprietary coating technique, customer-specified distribution functions are realized into a custom Bullseye® apodizing optical component that accounts for uniformity variations, substrate type, substrate size, and spectral bandwidth. Custom quotes are available.

Normal Gaussian distribution functions are defined by the following equations, where 'a' defines the standard deviation or the sharpness of the edges, and 'x' is the position of the function around the center of the component:


                                  bullseye inverse equation                                                                    bullseye equation

continuous variable inverse apodizing filter                                           Continuous variable bullseye apodizing filter

                        Bullseye® Inverse Apodizing filter                                                  Bullseye® Apodizing filter


The transition functions can be defined by either transmission (T) or by density (D).  These functions can range from a simple linear equation to much more complex algebraic, exponential, or geometric functions as shown below:                                       

Examples of Transmission Gradients:

 bullseye-transmission-gradients 2                                    


Examples of Density Gradients:

bullseye density gradients

Bullseye® Apodizing filters key features include:   

  • Density gradients can be customized to suit any application
  • The filter can be applied to a number of different substrate types and sizes
  • Filters can be designed to be used from the UV to the Far IR


Applications for Bullseye® Apodizing filters are found in diverse industries:  

  • Astronomy - To reduce high intensity light sources around the featured object.
  • Entertainment - To make light distribution uneven for cosmetic applications.
  • Imaging - To break up diffraction patterns by the introduction of soft edges.
  • Industrial - These filters are used in series with an iris camera to eliminate detector saturation that occurs in automatic welding machines.
  • Military - To eliminate IR detector saturation in ground-to-air and air-to-air missiles.
  • Photography - To create soft edges in photos and reduce areas that are over exposed.
  • Scientific - Used as a variable phase plate when the gradient coating material has the same index of refraction as the substrate.
  • Semiconductor - Used in exposing systems to obtain perfect illumination distribution.

We also offer custom Linear Apodizing filters, either dark or clear in the center.

Articles found on Photonics Spectra, Laser Focus World and Tech Briefs