Sensor Modules: the Camera
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Camera, whose interface is shown above, is the third basic sensor module. Camera ultimately outputs a quantity of the integrated intensity type. Important properties of Camera concerned with timing inputs, wavelength selectivity, multiple incident beams, spatial sampling and integration follow the principles discussed in the basic sensors overview. In the present section, we focus on the unique properties of Camera. Camera is more complicated than the previously discussed TargetBoard and SimpleFieldSensor, since Camera has two significant planes, namely an aperture and a sensor plane. Note that in the Camera interface names, "detector" refers to "sensor" plane.
In general terms, Camera forms a far-field image from the complex field incident on the module. Camera is characterized optically by itsfocalLength parameter. Based on the focal length value, Camera computes the complex field and then the intensity that is formed in the focal plane. More precisely, Camera takes the incident complex field, computes its space-domain Fourier transform, and outputs (const ·|transform|2). The factor (const) is constructed so that the output is the physical integrated intensity (J/m2) in the focal plane. The output variable is called fpaImage (fpa = focal-plane array), and the transverse mesh on which its values are reported is defined by the parameters (nxyDetector,dxyDetector).
The significance of the (nxyDetector, dxyDetector) specification is tricky. The transverse scale offpaImage is determined by the focalLength parameter, as follows. The complex field incident on Camera exists on the full propagation mesh (even though some values may be zeroed out by a preceding aperture): let the propagation mesh parameters be (nxyprop, dxyprop). Now, regardless of the (nxyDetector,dxyDetector) specs, the mesh spacing on which Camera's Fourier Transform result is internally computed is:
dxy_FT = [wavelength/(nxyprop·dxyprop)] · focaLength
Equivalently stated, a Discrete Fourier Transform operation is applied to the complex field on the entire incident mesh, and the result exists on a mesh whose parameters are (dxy_FT, nxyprop). Now, if we set the interface parameter dxyDetector = dxy_FT, then we would exploit the full available resolution of the Camera calculation. If desired, the user can subsample that result by setting dxyDetector to a coarser spacing than dxy_FT. Whether the user wants to subsample or not will usually depend on the dimension of the physical aperture that is placed in front of Camera. This physical aperture is discussed next.
CAUTION: dxyDetector in Camera has the following potentially confusing aspect. If dxyDetector is coarser than dxy_FT, then LightLike's reported fpaImage values are simply point-interpolated from the original |transform|2 values on the dxy_FT mesh. This is NOT equivalent to spatially integrating the irradiance over physical pixels whose size is dxyDetector. Depending on the physical system, such a spatial integration may be critical to a physically valid model of camera output. Spatial integration of that sort must be accomplished with an extra LightLike component.
Defining the aperture for Camera, and adjusting the image plane
CAUTION: another potentially confusing aspect of the Camera (and certain other imaging sensors, like HartmannWfsDft), is the interface parameter pair (nxyPupil, dxyPupil). From their names, one might think that these parameters actually specify a camera pupil size, but that is NOT the meaning. These two parameters are only used in conjunction with the technique of "wavesharing", which is an advanced option that attempts to eliminate redundant propagations that can occur in LightLike when multiple sensors are present. (We recommend that users become very familiar with LightLike before attempting to use wavesharing.) Unless wavesharing is being used, the parameters (nxyPupil, dxyPupil) have absolutely NO effect. However, even if not used, they must be assigned some arbitrary numerical values, because all parameters and inputs must be assigned values.
In order to define the physical entrance pupil (aperture) for a Camera module, the user must insert an Aperture or related module in front of the Camera. For a reason to be explained now, the Telescope module is frequently used for this purpose. The following illustration shows, in the top panel, the interface of Telescope, and in the lower panel, the contents of Telescope.
We see that Telescope consists of an Aperture module and a Focus module. In the present context, the purpose of the Focus module is to compensate for the fact that the source of the wave being imaged by Camera may be at some finite distance instead of infinity. The Fourier Transform computation of Camera, with the focalLengthspecified in Camera, gives the field in the focal plane corresponding to the field in the entrance plane of the Camera module. Typically (though not always) what is wanted as the Camera output is the intensity in the imageplane of the source. Therefore, we must add an extra (usually small) focus increment in order to make the image plane of the net system (Focus + Camera) coincide with the focal plane of Camera. This is achieved if we set therange parameter in Telescope equal to the object distance. The clearest way of understanding this is that a Telescope focus equal to the object range will collimate a point source located at the object: subsequently, this collimated wave entering Camera is focused at the focal plane of Camera, which means that the focal plane of Camera is now the image plane of the source. The user can of course insert separate Aperture and Focus modules to achieve the purpose described here, but the Telescope system provides a convenient combination module.