Note: Enabling Extended Range does not change system gamma or HDR Reference White. System gamma is adjusted according to the nominal peak luminance LW (the 100% signal level) through the formulas in ITU-R BT.2100-3 Note 5f, and HDR Reference White follows from LW and system gamma through the EOTF; neither input changes when the displayed range changes. Signals from 100% to 109% are "super-whites": they pass through the same EOTF, and displaying them requires headroom above the nominal peak.
"During production, signal values are expected to exceed the range E′ = [0.0 : 1.0]. This provides processing headroom and avoids signal degradation during cascaded processing. Such values of E′, below 0.0 or exceeding 1.0, should not be clipped during production and exchange."
Note: The slider now sets the display's Extended Peak Luminance. Rather than mapping the 100% nominal signal to the display peak, the 109% Extended Range signal is mapped to it. No direct formula gives the nominal peak luminance LW (the 100% signal level): system gamma depends on LW, the EOTF output at 109% depends on system gamma, and the 109% luminance is the product of LW and that EOTF output. This is why the nominal peak value has to be calculated from the extended peak value using an iterative solver:
\text{find } L_W \text{ such that } L_W \times \text{EOTF}_{\gamma(L_W)}[1.090183] = L_{109\%}
The solver uses bisection: the 109% luminance always increases with LW, so the solution is bracketed between a low and a high estimate, and the interval is halved repeatedly, keeping the half where the 109% luminance still fits within the display peak, until the two estimates agree.
System gamma and HDR Reference White are derived from the calculated, lower nominal LW. Lowering the effective nominal peak is the adjustment described in ITU-R BT.2100-3 Note 5f:
"For displays with nominal peak luminance (LW) other than 1 000 cd/m², or where the effective nominal peak luminance is adjusted through the use of a contrast control, the system gamma value should be adjusted according to the formula below and may be rounded to three significant digits: \gamma = 1.2 + 0.42\,\log_{10}(L_W/1\,000) For applications outside of the usual production monitoring range of LW equal to 400 cd/m² to 2 000 cd/m², the following extended range formula should be used:" \gamma = 1.2 \times \kappa^{\log_2(L_W/1\,000)} \text{ where } \kappa = 1.111
| Surround LuminanceInput | 5 cd/m² |
|---|---|
| Nominal Peak Luminance (100%)Input | 1000 cd/m² |
| Extended Peak Luminance (109%)Calculated | |
| Black LevelInput | 0.005 cd/m² |
| Black Level Lift (β)Calculated | 0.000 |
| System GammaCalculated | 1.20 |
| HDR Reference White (75%)Calculated | 203 cd/m² |
"The mapping of the camera sensor signal output to E may be chosen to achieve the desired brightness of the scene."
This HLG Display Adaptation Calculator implements the Hybrid Log-Gamma (HLG) system as specified in ITU-R BT.2100-3, with calculations for system gamma and HDR Reference White following ITU-R BT.2100-3 Note 5f, ITU-R BT.2390-12 Section 6.2 and ITU-R BT.2408-9 Section 2.1 respectively.
The intention is to help users understand more about how the Hybrid Log-Gamma (HLG) system works.
The idea for this tool was inspired by work related to EBU Recommendation R 167 - Reference Monitors: Predefined Modes for HLG.
Hybrid Log-Gamma (HLG) is one of two High Dynamic Range (HDR) formats defined in ITU-R BT.2100-3. HLG was created by the BBC and NHK. It is designed to adapt to displays with different peak luminance capabilities under different viewing conditions, ensuring a consistent perceptual experience on a wide range of devices without requiring metadata or additional processing.
HLG is a relative scene light to log transfer function. Unlike PQ (Perceptual Quantizer), which encodes absolute display luminance values, HLG maintains relative scene luminance relationships while allowing adaptation to different nominal peak luminance values.
HLG achieves this by applying a transfer function that blends characteristics of both traditional SDR gamma encoding and logarithmic HDR encoding.
HLG adapts to different display luminance levels and ambient lighting conditions, ensuring a consistent visual perception of brightness across different displays. This adaptability makes it future-proof, as HLG content will scale naturally with advancements in display technology.
HLG does not require metadata, which simplifies production, distribution, and device compatibility. Additionally, HLG is better suited as an archive format, as HLG is based on relative brightness, eliminating the need for regrading/remastering or metadata-dependent tone mapping as display technology evolves.
HLG is well suited for live HDR production workflows. It eliminates the need for complex metadata processing, making it the preferred HDR format for live HDR production and broadcast. A common approach for live HDR production today is the "single-master" HDR production workflow with SDR shading - documented in ITU-R BT.2408-9 Section 7.3.2, HLG production with SDR shading.
The human visual system responds logarithmically to light and adapts to different viewing conditions. Recognizing that people view content on various displays in widely different viewing environments, HLG was designed with this in mind.
When either peak luminance of the display or the viewing environment surround luminance change, the HLG system gamma is calculated and adjusted according to the formulas specified in ITU-R BT.2100-3, Note 5f and ITU-R BT.2390-12 Section 6.2.
That adaptive behaviour is precisely what this HLG Display Adaptation Calculator aims to demonstrate - as nominal peak luminance or surround luminance changes, the system gamma and resulting HDR Reference White luminance value automatically adjust to maintain a consistent perceptual appearance.
In professional environments, adjustment of nominal peak luminance might be necessary when:
“The most important aspect of any TV system is the OOTF”
High Dynamic Range (HDR) content created for broadcast and home entertainment should be displayed in a way that remains visually consistent across different peak luminance values and ambient conditions. This is achieved through the Opto-Optical Transfer Function (OOTF), which maps relative scene-referred light to displayed light:
\text{displayed light} \propto \text{scene light}^{\gamma}
where:
HLG adapts to different nominal peak luminance values and surround viewing conditions.
The HLG Reference OETF is a piecewise function that transforms scene linear light to the non-linear HLG signal. It consists of:
This hybrid approach preserves detail in shadows with the square-root segment while providing extended highlight range with the logarithmic segment.
The Inverse OETF converts the non-linear HLG signal back to scene linear light. It's the first step in the EOTF (Electro-Optical Transfer Function) chain, before applying the OOTF (Opto-Optical Transfer Function).
For the HLG system, the inverse OETF is defined as:
Where a, b, and c are constants defined in ITU-R BT.2100-3:
As explained in ITU-R BT.2390-12 Section 6.2, the light output of a television display is not proportional to the light detected by the camera. The overall system non-linearity, or "rendering intent," is defined by the opto-optical transfer function (OOTF). The OOTF maps relative scene linear light to display linear light to compensate for the psychovisual effects of watching an emissive screen in a dark or dim environment.
For HLG the OOTF is applied to the luminance component only, rather than independently to each color component as done in SDR television. This approach prevents color saturation and hue distortions that would otherwise occur when adapting content to displays of different peak luminance. According to ITU-R BT.2100-3 Table 5, the HLG reference OOTF is therefore given by:
Where the scene luminance is calculated as:
And the displayed RGB components are:
Where:
The complete HLG Reference EOTF process consists of three conceptual steps:
This process ensures that HLG content maintains perceptual consistency across different display technologies and viewing environments.
HLG adapts system gamma γ based on the display's nominal peak luminance LW and the surrounding viewing conditions. This ensures consistent perceptual brightness across different display technologies. The calculation follows the recommendations of ITU-R BT.2100-3 and ITU-R BT.2390-12.
The nominal peak luminance value of 1000 cd/m² in the formula for the HLG system gamma is used as a reference condition. It is not a signal constraint. When the BBC and NHK were developing HLG, both ran subjective tests to find the system gamma for a 1000 cd/m² display: NHK found an average preferred value of 1.18 on a 1000 cd/m² OLED, and the BBC found 1.29 for the best SDR-compatible picture. Weighing HDR production over SDR compatibility, a value of 1.2 was adopted for the reference 1000 cd/m² display in a 5 cd/m² surround (ITU-R BT.2390-12 Section 6.2). This configuration became HLG's reference condition, serving as the baseline from which all other viewing conditions are measured and calculated.
ITU-R BT.2100-3 Note 5f defines two formulas for adjusting the system gamma based on the nominal peak luminance (L_W), with different formulas optimized for different luminance ranges:
For displays within the usual production monitoring range (400 cd/m² ≤ L_W ≤ 2000 cd/m²):
For displays outside the usual production monitoring range (L_W < 400 cd/m² or L_W > 2000 cd/m²):
Both formulas are centered around the reference point of 1000 cd/m², where they produce identical results with a system gamma of 1.2. The second formula is based on a logarithmic power law and provides better performance at extreme luminance values. Within the 400–2000 cd/m² range, ITU-R BT.2390-12 Section 6.2 notes that the two models are "virtually identical and will provide equally good performance".
In addition to peak luminance adjustment, ITU-R BT.2390 Section 6.2 describes how system gamma should be reduced when the viewing environment is brighter than the 5 cd/m² reference surround. The Report presents two models for this; the calculator implements the multiplicative model with the surround luminance compensation factor (\mu), which can be applied to either of the above formulas:
Combining this with either of the baseline formulas gives the complete formula for system gamma:
For displays within the usual production monitoring range (400 cd/m² ≤ L_W ≤ 2000 cd/m²):
For displays outside the usual production monitoring range (L_W < 400 cd/m² or L_W > 2000 cd/m²):
Base gamma value for reference conditions: display at 1000 cd/m² in a 5 cd/m² surround
Adjusts gamma based on nominal peak luminance relative to reference
Adjusts gamma based on viewing environment relative to reference luminance
| Label | Value | Description |
|---|---|---|
| \gamma_{\text{ref}} | 1.2 | Reference system gamma with a 1000 cd/m² peak luminance display |
| \kappa | 1.111 | Peak luminance adaptation factor of the extended-range formula (ITU-R BT.2100-3, Note 5f) |
| L_W | (cd/m²) | Nominal peak luminance of the display in cd/m² |
| L_{\text{ref}} | 1000 | Reference peak luminance in cd/m² |
| \mu | 0.98 | Surround luminance compensation factor (ITU-R BT.2390-12, Section 6.2) |
| L_{surround} | (cd/m²) | Surround luminance in cd/m² |
| L_{surround\ ref} | 5 | Reference surround luminance in cd/m² (ITU-R BT.2100-3) |
The \kappa (kappa) value of 1.111 is an empirically derived coefficient (ITU-R BT.2100-3, Note 5f) that adjusts system gamma to maintain perceptual contrast consistency across different peak luminance levels. ITU-R BT.2390-12 Section 6.2 fits it to the BBC's subjective tests and attributes the extended model to Tim Borer's 2017 paper on the display of HDR images under varying viewing conditions (BBC R&D WHP 369), which also introduces the surround model below.
The \mu (mu) value of 0.98 is a compensation factor (ITU-R BT.2390-12, Section 6.2) that adjusts system gamma based on surround luminance, ensuring perceptual consistency in different viewing environments.
Under reference conditions, with a 1000 cd/m² peak luminance display with 5 cd/m² surround luminance, both ratios equal 1, resulting in the reference gamma of 1.2.
ITU-R BT.2408-9 defines "HDR Reference White" as the nominal signal level obtained from an HDR camera and a 100% reflectance white card, also known as "Diffuse White." This represents a guiding reference point in the HDR signal, where the luminance range above it provides headroom for specular highlights and emissive sources.
According to ITU-R BT.2408-9, the HDR Reference White point corresponds to a signal level of 75% for HLG and 58% for PQ. For PQ, which encodes absolute luminance values, the 58% signal value always represents 203 cd/m². For HLG, a signal level of 75% produces a luminance of 203 cd/m² when displayed on a reference monitor with 1000 cd/m² peak luminance in a reference viewing environment of 5 cd/m² surround luminance, with the system gamma set to 1.2.
If the nominal peak luminance or surround luminance is changed, the HLG system gamma, and with it the luminance produced by the 75% signal, adjusts accordingly. The signal level itself does not change: as ITU-R BT.2408-9 notes, "The nominal signal levels in Table 1 do not change"; for HLG it is the nominal luminance values that vary with the display's peak luminance.
The 75% signal is first converted to the normalized linear scene luminance (YS) using the inverse OETF:
Where:
YS is scene luminance, not yet Reference White, which ITU-R BT.2408-9 defines as a display luminance. Applying the OOTF (ITU-R BT.2100-3 Table 5) with the achromatic signal E = YS, and the user gain α set to the nominal peak luminance LW, gives the Reference White luminance:
At the reference condition (LW = 1000 cd/m² and system gamma γ = 1.2), this yields 1000 × 0.26501.2 ≈ 203 cd/m², the HDR Reference White level in ITU-R BT.2408-9 Table 1. When black level lift is enabled, the 75% signal is first lifted (E' → max(0, (1−β)E' + β)) before the inverse OETF, so Reference White also depends slightly on β.
In practice, all display technologies have physical limitations that prevent them from producing absolutely perfect black (zero luminance):
The black level lift parameter (β) in the HLG system was specifically designed to address this reality. It mathematically adjusts how the HLG signal is mapped to display light output to compensate for these non-zero black levels. This ensures that content appears consistent across different displays with varying black level capabilities.
Without this adjustment, the same HLG content would appear differently on displays with different black level capabilities, with shadows and dark details being rendered inconsistently. The black level lift formula in ITU-R BT.2100-3 provides a standardized way to maintain perceptual consistency across diverse display technologies.
According to ITU-R BT.2100-3 Table 5, black level lift is defined as:
Where:
When black level lift is enabled, the HLG EOTF applies this adjustment to each signal component before further processing:
PLUGE, a term originally derived from "Picture Line Up Generating Equipment", is a standardized test signal defined in ITU-R BT.814-4 specifically designed for accurately setting black levels in display systems. The PLUGE test pattern contains bars slightly above and below reference black level, allowing engineers and users to properly calibrate the darkest parts of the image.
In the alignment procedure of ITU-R BT.814-4, the user black level lift control is adjusted so that the darker stripe just disappears while the lighter stripe remains visible. This ensures that shadow detail is preserved while maintaining proper black level performance.
The PLUGE calibration and black level lift parameter work together in a complete HLG display calibration workflow:
ITU-R BT.2100-3 (Table 3, Note 3d) specifically notes: "For PQ in a non-reference viewing environment, or for HLG (in any viewing environment), the black level should be adjusted using the PLUGE test signal and procedure specified in Recommendation ITU-R BT.814." This requirement ensures consistent rendering of dark tones across different display technologies.
Proper black level adjustment using PLUGE is particularly crucial for HLG implementations because HLG is a display-adaptive system. Unlike PQ which encodes absolute luminance values, HLG's adaptability requires accurate black level calibration to maintain perceptual consistency from content creation through to consumer viewing environments.
This combined approach ensures that black levels are properly rendered on displays where absolute zero luminance isn't achievable, maintaining perceptual consistency across different display technologies.
Professional reference monitors should allow toggling between Nominal Range (0-100%) and Extended Range (0-109%).
The Extended Range feature allows monitors to display "super-white" signals that extend beyond the nominal 100% signal level, up to 109%: the top of the headroom above nominal peak in EBU R 103 Figure 1, at 10-bit code 1019. R 103 notes that the term "extended range" for the 64–1019 code range is in use but not formally defined. This provides slightly increased dynamic range for HLG content and can allow viewers to see highlight detail that would otherwise be clipped.
In order to display the Extended Range above the specified peak reference level for 100% signal, the display must have sufficient headroom above its stated peak luminance to allow for 109% to be displayed.
The normalized signal ratio for Extended Range can be calculated using the 10-bit Narrow Range digital code values:
Where:
The HLG transfer functions in ITU-R BT.2100-3 Table 5 are specified for signals up to E' = 1, but such super-white signals are anticipated by the Recommendation: Note 5h states that during production "signal values are expected to exceed the range E' = [0.0 : 1.0]" and that they "should not be clipped during production and exchange". The luminance calculation below therefore applies the same EOTF to the 109% signal.
To calculate the absolute luminance produced by the 109% signal, we apply the complete HLG EOTF, whose OOTF carries the user gain α = LW (ITU-R BT.2100-3 Table 5). For an achromatic signal this is:
Where:
v1.6, Concept and implementation by Thomas Berglund (NRK), based on EBU Recommendation R 167. Source available under the Apache License 2.0.