Narcissus

“Nasrcissus” Origin 

Narcissus and Echo at the Reflection Pool (1)

In Greek mythology, Narcissus is a young man who fell in love with himself after seeing his reflection in a pool of water. He obsessed over this by continually revisiting the pool to view his reflection, all the  while, spurning  the advances of the beautiful maiden, Echo.

Today, the word, narcissism denotes  self-centeredness, and  vanity, especially in the form of excessively  looking into a mirror to see oneself.

Narcissus in Infrared Cameras

In a modern infrared camera,  the detector can see an image of itself in addition to  an image of the intended scene. This results in  ” narcissus” , an aptly named undesirable image artifact. common in infrared cameras.

In general,  there are several such images of the detector on itself, each corresponding to a lens surface reflection.. The images are usually out of focus by varying degrees. The summation of all such images on the detector results in a central “cold spot”. in the displayed image.

Image from an Infrared Camera (2)

The cold spot is due largely  to  the detector being  cooled  to a  temperature well below room temperature. As shown at the left, the image of the detector created  from a reflection off a  lens surface of even very  low reflectance and  in which the image is usually far  out of focus on the detector, still can readily be seen superimposed on the scene image under certain conditions. 

In this example, a  blackish circular spot can be seen where the person’s  finger is pointing  Note that the spot does not appear as a uniform black circular spot.This is because the area within  the spot consists of the sum of the narcissus image of the detector  and the scene image,  the latter  consisting of a mix of image elements of varying temperature and emissivity. Where the difference in temperature and / or emissivity  between the narcissus image and scene image is significantly different, then the  narcissus image becomes visible, as in the drapery in the background in this picture.

The picture at the right shows the narcissus image when the camera looks at a pure, uniform  blackbody source.The narcissus image is clearly shown as the centrally located button-like artifact.

Narcissus image of a uniform blackbody (3)

The appearance of narcissus can vary depending on display system settings,

System gain and offset setting can show  narcissus to a greater or less degree, A system  setting  for resolving greater scene thermal detail is sometimes results in the unwanted   narcissus..

The following  discussion focuses on showing precisely how the narcissus image is created  and how it is assessed using ray trace analyses of an infrared camera  lens..

Infrared Camera Objective Lens & Detector

The lens illustrated below is a wide field of view  infrared objective lens which will be assumed for the forthcoming narcissus analysis. Lens materials typically include germanium, silicon and other visually opaque materials. The detector is an array of sensor image elements or “pixels”.. Arrays are typical 10-12 mm in size with sensor elements or “pixels” about 10 microns square. A cold stop, which is the optical system aperture stop is located within the detector dewar.  Its diameter and distance from the detector  define the system  f-number.

 

The dewar also houses a cold filter which reduces narcissus by limiting the spectrum of rays which reach the detector  to  include only those which lie  within the scene spectrum of interest. Thus rays lying outside this spectrum which originate within the lens housing and are.reflected from lens surfaces are  excluded from reaching the detector, thereby reducing narcissus accordingly.

The dewar vacuum is preserved by the dewar window. The detector is cooled to 77° K to achieve high thermal sensitivity to incoming photons from the scene. The detector is cooled by a Sterling type miniature cooling engine with cold “finger” in contact with the detector. Infrared cameras of this type provide viewing in total darkness in either the 3-5 micron or 8-12 micron wavebands.

IR Objective Lens Configuration for Narcissus Analysis

Since narcissus deals with the detector receiving an image of itself,  the lens configuration is reversed from its normal use position for the analysis. The detector serves as the object from which rays are emitted.  The rays are transmitted forward until reflection off a lens surface occurs and then are traced back to the detector to determine their intercept points on the detector.

In the illustration at the left, rays from a point on the detector travel forward through a filter and dewar window and are  then refracted by the first surface of the first lens encountered. After refraction by the first surface, the rays travel onward to the second surface which again refracts the rays but also reflects the rays backward towards the detector. After reflection the rays are transmitted rearward until they reach the detector. Of importance is the degree to which the rays are in focus at the detector, i.e., whether an  in-focus image of the detector exists or whether the image is weak and out-of-focus. The in-focus ghost image  is a strong contributor to narcissus, the latter a weaker one.

In this example, reflection from only one lens surface is considered. Actually, there is a similar situation with all lens surfaces. Further, in this example,  only the rays from a single point on the detector are considered, whereas, in a more  comprehensive analysis, rays from all points over the cooled detector surface are considered..

Ghost Images at the Detector

The illustration below shows ray traces of rays  originating  from two points on the detector,  one  on-axis, the other  off-axis.

Rays are emitted from the points and travel toward the lens..The system aperture stop located at the filter defines a cone of rays which proceed onward through the  filter and the dewar window towards  lens elements L3 and L2. The outer surface of  lens L2 is treated as a mirror to illustrate the process of ghost image formation. All other lens surfaces including those of lens L1, not shown here, also  generate ghost images by a similar process. 

The rays reflected by the outer surface of lens L2 are all directed back towards the detector from which they originated. However, not all of the reflected rays make their way back to the detector. Some are reflected to the region outside the clear aperture of the window, in this case, striking the lens or dewar window  housings where they are absorbed or diffusely reflected.

Other rays may not make it back due to total internal reflection  (TIR) encountered along the way. The illustration shows two such rays, the marginal rays of the axial ray bundle, truncated at the inner surface of  lens L2.

In other cases the reflected rays can  encounter  extreme  angles of incidence  resulting in extremely large  refraction and reflection  angles causing the rays to exceed the radius of the lens which they are directed towards.

These failure of the reflected rays to make their way  back to the detector is a  favorable outcome  regarding narcissus because fewer reflected rays are then present  at the detector to generate a strong narcissus image.

The out-of-focus ghost image from a detector object point is a circular spot of a certain diameter at the detector as indicated in the illustration. The spots are actually somewhat larger than indicated in the illustration because of the limited number of rays, chosen for clarity in this illustration. Other lens surfaces  create their own unique ghost image, some being far out of focus, some occasionally being quite near to perfect focus. Ghost images which are far out of focus are very desirable while in-focus ghost images can be disastrous, resulting in a very objectionable “cold spot” in the center of the displayed image..

In this example involving lens L2 oiuter surface as the ghost generating surface, the out-of-focus ghost image for on-axis and off-axis points happens to be about the same. However, this is not generally  the case. For example, a window located  in front of the lens  with its flat surfaces will generate a very strong  in-focus ghost image of the center of the detector, and much less so for points off-axis.

With a plano window surface  in front of the lens the angle of incidence of the marginal axial ray from the detector is zero causing the ray to be reflected back on the trajectory from which it came.. Within the lens, angles of incidence can approach zero, as well, leading to equally detrimental  narcissus.

Analyzing  Narcissus by Ray Trace of Ghost Images

To determine the narcissus  irradiance on the detector, each lens surface is treated, in sequence, as a mirror. Rays are traced from the originating point on the detector out to the mirror lens surface and back toward the detector. As shown above, many rays never make it back to the detector for various reasons.

One approach for analyzing a lens for narcissus is to launch many rays from points all over the detector towards the aperture stop. A cone of rays is generated at each of these field points by directing the cone towards the aperture stop. An imaginary  grid at the stop defines the rays launched from the field points. Thr circular aperture stop immediately reduces the number of rays within the rectangular grid  to only those that can pass through the circular stop, a number equal to approximately three quarters of the launched rays.

As illustrated at the left, tens of thousands of rays are used in the analysis.

A much smaller number make it back to the detector. The ray radial intercept  distance from the center of the detector is recorded for every ray.

When the ray traces for all ghost lens configurations are completed, the radial intercepts of all the rays on the detector focal plane are sorted into annular zones on the detector as shown below. The detector is represented by the rectangle; ghost image ray intercepts on  the detector by the dots.

Ghost ray intercepts on the detector sorted into annular zones

 

The illustration at the right  is an artist’s  concepton of what the distribution of rays on the focal plane might look like. The greatest density of ghost ray intercepts occurs at the  center of the detector format,

A ray trace of all the ghost images is performed  using optical design software such as Zemax.   After reversing the lens so that the detector becomes the object,  separate ghost lens configurations for each lens surface are generated by the program i.e. in each configuration  lens surfaces are changed sequentially  to act as  a mirror surface,  Rays are then traced from the detector out to the reflecting surface and back to the detector. Generally, only a small fraction of the rays launched from the detector make their way back due to  the various mechanisms discussed above. Zemax stores each ghost lens configuration as it would any other lens design file.

Rays are sorted into annular zones via a custom computer program based on the Zemax ZPL programming language. The macro, “Narcissus” is placed by the user  in the Zemax macro folder and appears in the macro dropdown list in the Zemax menu bar.  Details on operation of the macro can be found in Narcissus Macro Flowchart and Narcissus Operation Instructions.

The output from the macro consists of a table in which the narcissus relative irradiance is tabulated for ten annular zones on the detector and this is done for each ghost lens configuration that has been specified by the user. The sum of the irradiance for each zone is calculated and appears in the bottom row of the table.

The infrared objective lens presented above has been ray traced in this manner. Results appear in the table belowThe first column identifies the ghost lens configuration for the ray trace data in the following columns.

The second and third columns provide paraxial image ray angle and paraxial image heights at the detector  for the  axial marginal ray which is launched from the point at the center of the detector. This data gives a good indication of the ghost image effects on the narcissus irradiance on the detector….a .large ray height indicate large defocus, a favorable condition because it results in low narcissus irradiance .On the other hand,  the ray height for Surface 12 is nearly zero, indicating an in-focus condition, a very unfavorable condition. The in-focus return is caused by the flat surface of Surface 12 reflecting back the image which otherwise would be formed at infinity image distance.

The number of ray intercepts on the detector plane  for each annular zone appear in the  table with corresponding numbered columns.the  for each zone, weighted  by  the area of the zone. The resultant quantity is proportional to the irradiance, i.e., the radiant  flux per unit area.

Examination of the table reveals the relative contribution of each ghost surface to the total irradiance. Surface 9, for example, detailed in one of the above  illustrations, contributes very little irradiance to the total detector narcissus irradiance due to the large out-of-focus ghost image  that it creates. The rays for each zone are relatively low in number and fairly evenly distributed across the detector, both conditions favorable for low narcissus.

The bottom line presents the sums of the rays in each zone  for all of the ghost image lens configurations considered together.. This is the end product of the analysis: the relative narcissus irradiance across the detector image plane.

The relative irradiance can be converted to absolute values of noise equivalent  temperature difference by multiplication of a separately calculated value, “NARC_ΔT.

Acknowledgements

(1). “Echo and Narcissus” painting,  by John William Waterhouse

(2)  Image from an infrared camera, courtesy of FLIR Systems Inc., Wilsonville, Oregon

(3) Narcissus image of a uniform blackbody (ibid.)