Camera Flange Focal Distance Change Due to Inserted Windows and Filters

Why can the FFD be smaller than the distance separating the camera's flange and sensor?

Flange focal distance (FFD) values for cameras and lenses assume only air fills the space between the lens and the camera's sensor plane. If windows and / or filters are inserted between the lens and camera sensor, it may be necessary to increase the distance separating the camera's flange and sensor planes to a value beyond the specified FFD. A span equal to the FFD may be too short, because refraction through windows and filters bends the light's path and shifts the focal plane farther away.

If making changes to the optics between the lens and camera sensor, the resulting focal plane shift should be calculated to determine whether the separation between lens and camera should be adjusted to maintain good alignment. Note that good alignment is necessary for, but cannot guarantee, an in-focus image, since new optics may introduce aberrations and other effects resulting in unacceptable image quality. 

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Figure 2: Refraction causes the ray's angle with the optical axis to be shallower in the medium than in air (θ_m vs. θ_o ), due to the differences in refractive indices (n_m vs. n_o ). After travelling a distance d in the medium, the ray is only h_m closer to the axis. Due to this, the ray intersects the axis Δf beyond the f point. 

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Figure 1: A ray travelling through air intersects the optical axis at point f. The ray is h_o closer to the axis after it travels across distance d. The refractive index of the air is n_o .

Equations for Calculating the Focal Shift (Δf )
Angle of Ray in Air, from Lens f-Number ( f / N )
Change in Distance to Axis, Travelling through Air (Figure 1)
Angle of Ray to Axis, in the Medium (Figure 2)
Change in Distance to Axis, Travelling through Optic (Figure 2)
Focal Shift Caused by Refraction through Medium (Figure 2)	Exact Calculation
	Paraxial Approximation

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Figure 4: Tolerance and / or temperature effects may result in the lens and camera having different FFDs. If the FFD of the lens is shorter, images of objects at infinity will be excluded from the focal range. Since the system cannot focus on them, they will be blurry. 

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Figure 3: When their flange focal distances (FFD) are the same, the camera's sensor plane and the lens' focal plane are perfectly aligned. Images of objects at infinity coincide with one limit of the system's focal range.

A Case of the Bends: Focal Shift Due to Refraction
While travelling through a solid medium, a ray's path is straight (Figure 1). Its angle (θ_o ) with the optical axis is constant as it converges to the focal point (f ). Values of FFD are determined assuming this medium is air.

When an optic with plane-parallel sides and a higher refractive index (n_m ) is placed in the ray's path, refraction causes the ray to bend and take a shallower angle (θ_m ) through the optic. This angle can be determined from Snell's law, as described in the table and illustrated in Figure 2. 

While travelling through the optic, the ray approaches the optical axis at a slower rate than a ray travelling the same distance in air. After exiting the optic, the ray's angle with the axis is again θ_o , the same as a ray that did not pass through the optic. However, the ray exits the optic farther away from the axis than if it had never passed through it. Since the ray refracted by the optic is farther away, it crosses the axis at a point shifted Δf beyond the other ray's crossing. Increasing the optic's thickness widens the separation between the two rays, which increases Δf.

To Infinity and Beyond
It is important to many applications that the camera system be capable of capturing high-quality images of objects at infinity. Rays from these objects are parallel and focused to a point closer to the lens than rays from closer objects (Figure 3). The FFDs of cameras and lenses are defined so the focal point of rays from infinitely distant objects will align with the camera's sensor plane. When a lens has an adjustable focal range, objects at infinity are in focus at one end of the range and closer objects are in focus at the other.

Different effects, including temperature changes and tolerance stacking, can result in the lens and / or camera not exactly meeting the FFD specification. When the lens' actual FFD is shorter than the camera's, the camera system can no longer obtain sharp images of objects at infinity (Figure 4). This offset can also result if an optic is removed from between the lens and camera sensor.

An approach some lenses use to compensate for this is to allow the user to vary the lens focus to points "beyond" infinity. This does not refer to a physical distance, it just allows the lens to push its focal plane farther away. Thorlabs' Kiralux™ and Quantalux^® cameras include adjustable C-mount adapters to allow the spacing to be tuned as needed.

If the lens' FFD is larger than the camera's, images of objects at infinity fall within the system's focal range, but some closer objects that should be within this range will be excluded. This situation can be caused by inserting optics between the lens and camera sensor. If objects at infinity can still be imaged, this can often be acceptable.

Not Just Theory: Camera Design Example
The C-mount, hermetically sealed, and TE-cooled Quantalux camera has a fixed 18.1 mm spacing between its flange surface and sensor plane. However, the FFD (f ) for C-mount camera systems is 17.526 mm. The camera's need for greater spacing becomes apparent when the focal shift due to the window soldered into the hermetic cover and the glass covering the sensor are taken into account. The results recorded in the table beneath Figure 2 show that both exact and paraxial equations return a required total spacing of 18.1 mm.