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The perceptual quantizer (PQ), published by SMPTE as SMPTE ST 2084,^[1] is a transfer function that allows for HDR display by replacing the gamma curve used in SDR.^[2][3][4][5] Its 0–1 value range represents luminance levels from 0 to 10,000 cd/m² (nits).^[2] It was developed by Dolby^[6] and standardized in 2014 by SMPTE^[1] and also in 2016 by ITU in Rec. 2100.^[7][8] ITU specifies the use of PQ or HLG as transfer functions for HDR-TV.^[7] PQ is the basis of HDR video formats (such as Dolby Vision,^[2][9] HDR10^[10] and HDR10+^[11]) and is also used for HDR still picture formats.^[12][13] PQ is not backward compatible with the BT.1886 EOTF (i.e. the gamma curve of SDR), while HLG is compatible.

PQ is a non-linear transfer function based on the human visual perception of banding and is able to produce no visible banding in 12 bits.^[14] A power function (used as EOTFs in standard dynamic range applications) extended to 10000 cd/m² would have required 15 bits.^[14]

The PQ EOTF (electro-optical transfer function) is as follows:^[7][15]

$F_D=EOTF\left[E^{\prime }\right]=10000{\left(\frac{max\left[\right(E{\text{'}}^{1/m_2}-c_1),0]}{c_2-c_3\cdot E{\text{'}}^{1/m_2}}\right)}^{1/m_1}$

The PQ inverse EOTF is as follows:

$E^{\prime }=EOT{F}^{-1}\left[F_D\right]={\left(\frac{c_1+c_2\cdot Y^{m_1}}{1+c_3\cdot Y^{m_1}}\right)}^{m_2}$

where

• $E^{\prime }$ is the non-linear signal value, in the range $[0,1]$.
• $F_D$ is the displayed luminance in cd/m²
• $Y=F_D/10000$ is the normalized linear displayed value, in the range [0:1] (with $Y=1$ representing the peak luminance of 10000 cd/m²)
• $m_1=\frac{2610}{16384}=\frac{1305}{8192}=0.1593017578125$
• $m_2=128\frac{2523}{4096}=\frac{2523}{32}=78.84375$

• $c_1=\frac{3424}{4096}=\frac{107}{128}=0.8359375=c_3-c_2+1$
• $c_2=32\frac{2413}{4096}=\frac{2413}{128}=18.8515625$
• $c_3=32\frac{2392}{4096}=\frac{2392}{128}=18.6875$

• Transfer functions in imaging
• High-dynamic-range television