# Operation of Variable Neutral Density Filters

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Operation of Variable Neutral Density Filters

Hi Folks,

Variable Neutral Density filters do - somewhat, see below - what they say.

They are primarily used for shooting video, particularly video that is somewhat "run-and-gun", where the scene cannot be blocked, and rapid changes in attenuation are required. An example might be wildlife photography, where the camera operator is following the subject through broken woodland. Some minor losses in sharpness and colour accuracy relative to good-quality fixed ND filters are accepted in exchange for convenience in the field.

The basic principle of operation is crossed polarisers: If the polarisers are parallel, they let light through; if they are crossed, they block light. [Some of you may see a problem already... ]

My understanding of how to use some kinds of variable ND ("VND") filters differs from some of the manufacturers recomendations, and from descriptions on the interwibble.

I'd be grateful if folk could tell be what I'm missing, or if I have the right idea. I'm a bit rusty on the maths and physics of polarisation.

These are VND filters screwed to the front of the lens.

To make life simpler, to avoid getting sidetracked in second order details, to start with at least, can we assume:

• Polarising filters work perfectly across the optical frequency band, understood to include all frequencies to which the sensor might be sensitive.
• Any Quarter-Wave-Plates ("QWP") provide a precise lambda/4 aka pi/2 phase difference between slow and fast axes across the optical frequency band.
• Where QWPs and polarisers are physically bonded to each other, the axes of the polariser perfectly bisect the fast and slow axes of the QWP.
• The two polarising elements can rotate only between parallel polarisation, and a few degrees short of cross polarisation. [Often there are no stops limiting rotation between the polarisers, but this assumption covers practical cases, and perhaps makes some arguments simpler]

Constructions for VND filters:

There seem to be a few common kinds:

1. Scene ->QWP->polariser->mechanical rotation->polariser->QWP->lens
2. Scene ->polariser->mechanical rotation->polariser->QWP->lens
3. Scene ->polariser->mechanical rotation->polariser->QWP->mechanical rotation->lens

The final QWP seems to be a concession to SLR autofocus and metering, though AFAICT VND filters are mainly used for video.

Marks on the holders of the first and second elements almost invariably advertise an attenuation scale: a "Minimum" mark indicates that the polarisers are parallel; a "Maximum" mark indicates that the polarisers are nearly crossed. Sometimes a numerical scale between "Min" and "Max" is present, usually marked in arbitrary units with constant angular spacing. The front element may rotate freely, or there may be stops at the "Min" and "Max" positions.

Examples:

1: Front and rear QWPs:

2: Rear QWP only; orientation of rear polariser fixed if filter is screwed in:

3: Rear QWP only; polarisers can be rotated independently:

Filters of type (3) are advertised as providing control of both polarisation and attenuation.

The polarising effect of filters of type (2) is not advertised. These are usually the cheapest VND filters.

Behaviour:

[Propositions I understand as true]

1. Given a scene reflecting unpolarised light towards the camera, all three constructions behave similarly: attenuation is adjusted by changing the angle between the two polarisers. The orientation of the polarisers relative to the scene does not matter.
2. Only filters of type (1) (front QWP) behave as polarisation-neutral VNDs. Any scene polarisation is removed (replaced with circular polarisation).
3. In any VND, selection of polarisation is only controlled if the first (front) element is a polariser, not a QWP.
4. If polarisation control is available (no front QWP), it is only available via rotation of the front element. [This may seem stunningly obvious, but is contradicted by both reviews, and some manufacturers' instructions].
5. If the orientation of the front polariser (no front QWP) is fixed, rotating the second polariser has a purely ND effect: there are no relative changes in intensity of different parts of the scene.
6. (No front QWP) If the orientation of the second polariser is fixed, rotating the front polariser in the marked direction of increasing attenuation may increase or decrease the intensity of scene elements, depending on the polarision of light reflected towards the camera by these elements. Similarly, rotating the front polariser in the marked direction of decreasing attenuation may decrease or increase the intensity of scene elements. Maximum transmission might occur half-way between the "Min" and "Max" attenuation markings. This is a manifestation of the "Three polariser Paradox": the user has a polarisation rotator, not a variable ND filter.

Have I got those right?

Implications for use:

1. In filters with no front QWP, rotating the front element while leaving the rear element fixed with the intent of changing overall scene attenuation will cause both hue shifts and relative intensity changes within a scene which reflects polarised light (i.e. much or most of the time).
2. In filters with no front QWP, and two rotating stages, control of both polarisation and attenuation can be acheived by (a) rotating the front element to achieve the desired polarisation effect, and then (b) rotating the rear element - while keeping the orientation of the front element fixed - to achieve the desired attenuation.
3. Filters with no front QWP, and only one rotator can be fairly easily converted to filters with two rotators by screwing the mount for a cheap circular polarising filter or ND grad onto the back (after removing the retaining ring and filter glass from the cheap filter). Amazon Basics Circular Polarizer works for me. [Oddly, the Amazon CIR-PL is really not bad. Not the very best, but better than many far more expensive filters]. The downside of this is increased hard vignetting with wide angle (never mind UWA) lenses.