PQ Perceptual Quantizer (SMPTE ST 2084)

Definition and origin

An EOTF — Electro-Optical Transfer Function — is the curve a display applies to convert an incoming digital code value into a specific emitted luminance. SDR televisions used a gamma curve for this job; HDR introduced a new family of EOTFs, of which the Perceptual Quantizer is the most widely deployed. The companion concept on the encode side is the OETF, the Opto-Electronic Transfer Function.

PQ was developed at Dolby Laboratories. The foundational paper, "Perceptual Signal Coding for More Efficient Usage of Bit Codes" by Scott Miller, Mahdi Nezamabadi, and Scott Daly, was presented at the 2012 SMPTE Annual Technical Conference and published in the SMPTE Motion Imaging Journal in May 2013. SMPTE then ratified the curve as ST 2084 in 2014, under the formal title "High Dynamic Range Electro-Optical Transfer Function of Mastering Reference Displays." The standard text itself is paywalled; readers needing the exact mathematical form should consult ST 2084 directly or its parallel publication in ITU-R BT.2100.

Design and bit-efficiency

PQ's shape is not arbitrary. Dolby derived it from P. G. J. Barten's 1999 model of the human contrast-sensitivity function, which estimates the smallest luminance step a viewer can detect — the just-noticeable difference, or JND — at any given adaptation level. The PQ curve is engineered so that successive code values fall just below that JND threshold across the encoded range. The practical payoff is bit efficiency: PQ produces no visible banding from 0 to 10,000 nits using 12 bits of precision, where a naive power-function gamma extended to the same 10,000-nit ceiling would have required roughly 15 bits to behave as well.

The other defining choice is that PQ is absolute and display-referred. Every input code value corresponds to a specific output luminance in nits that the display is intended to reproduce exactly. Code 0 is 0 nits, the top of the curve is 10,000 nits, and the values in between are pinned to that scale rather than scaled by whatever peak the panel can hit. The 10,000-nit ceiling is a property of the curve, not of any consumer display — virtually no shipping TV reaches it. That asymmetry between what PQ can describe and what a panel can emit is the reason tone mapping is such a load-bearing piece of the rest of the pipeline.

Standards and HDR-format ecosystem

Beyond SMPTE ST 2084, PQ is also published in ITU-R Recommendation BT.2100, posted by the ITU on 4 July 2016. BT.2100 is the international HDR-TV image-parameter recommendation, and it defines two HDR transfer functions: PQ and Hybrid Log-Gamma (HLG). It specifies bit depths of either 10 or 12 bits per sample.

On the content side, PQ is the EOTF underneath all three of the major delivery formats: HDR10 (10-bit, ST 2086 static metadata, announced August 2015), HDR10+ (10-bit plus ST 2094-40 dynamic metadata), and Dolby Vision (up to 12-bit plus ST 2094-10 dynamic metadata, peak luminance up to 10,000 nits). What separates these formats from one another at delivery time is metadata, not the underlying transfer curve.

The notable exception is HLG, the broadcast-oriented HDR transfer function co-developed by the BBC and NHK. HLG is relative and scene-referred: the same signal scales naturally between SDR and HDR receivers based on the display's peak luminance, which suits live broadcast in a way an absolute curve does not. BT.2100 publishes HLG and PQ side by side as alternatives. PQ is a luminance specification only — it does not define color primaries. In practice it is paired with the BT.2020 wide color gamut (identical to the BT.2100 primaries), and HDR10, HDR10+, and Dolby Vision all combine PQ with those primaries.

Tone mapping on consumer displays

Because PQ encodes up to 10,000 nits but no shipping consumer TV reaches that peak, every PQ-encoded delivery has to be tone-mapped at the display. Highlights brighter than the panel's actual peak luminance are compressed or rolled off so they remain on screen rather than being hard-clipped to white. Tone mapping is therefore a mandatory step in any real-world PQ pipeline.

How well that compression goes depends largely on what the display knows about the content. HDR10 carries a single set of static metadata for the entire program: SMPTE ST 2086 mastering-display volume (primaries, white point, min and max luminance) plus MaxCLL — the brightest single pixel anywhere in the program, in nits — and MaxFALL, the highest frame-average light level. The display chooses one fixed tone-mapping curve from those whole-program numbers and lives with it for the duration.

Dynamic metadata changes that calculus. Dolby Vision (using SMPTE ST 2094-10) and HDR10+ (using SMPTE ST 2094-40) attach updated brightness statistics on a scene-by-scene or frame-by-frame basis, so the display can recompute its tone-mapping curve as content changes. A 1,000-nit panel can preserve highlight detail in a bright daylight exterior without crushing shadow detail in the next dim interior — something a single program-wide MaxCLL/MaxFALL pair simply cannot describe.