ColorBarsUHD¶

ColorBarsUHD generates a video clip containing UHD/HDR colour bars conforming to Rec. ITU-R BT.2111-3 (05/2025). Three signal variants are available via the mode parameter, corresponding to the three pattern subtypes defined in BT.2111-3.

For SDR color bars see ColorBars and ColorBarsHD filters.

By default, a 3840×2160, RGBP10, limited-range, 29.97 fps, 1-hour-long clip is produced. The height is automatically derived from the width to maintain the 16:9 aspect ratio of the standard 3840×2160 reference.

Audio is also generated — see the audio section in ColorBars / ColorBarsHD for details.

../../_images/colorbarsuhd_mode0_hlg.png — ColorBarsUHD mode=0: HLG narrow range (BT.2111-3 Table 2). 75% primary colour bars. RGBP10, limited range. *(Rendered to 8-bit for display purposes.)*¶

../../_images/colorbarsuhd_mode1_pqnarrow.png — ColorBarsUHD mode=1: PQ narrow range (BT.2111-3 Table 3). 58% primary colour bars with 100% top row. RGBP10, limited range. *(Rendered to 8-bit for display purposes.)*¶

../../_images/colorbarsuhd_mode2_pqfull.png — ColorBarsUHD mode=2: PQ full range (BT.2111-3 Table 4). 58% primary colour bars with 100% top row. RGBP10, full range. *(Rendered to 8-bit for display purposes.)*¶

../../_images/colorbarsuhd_hlgtosdr.png — ColorBarsUHD mode=0 (HLG) converted to SDR/BT.709 using fmtconv display-referred path (ITU Fig. 12), `lws=1000` (γ=1.2, reference 1000 cd/m² display). *(Rendered to 8-bit for display purposes.)*¶

../../_images/colorbarsuhd_hlgtosdr10000.png — ColorBarsUHD mode=0 (HLG) converted to SDR/BT.709 using fmtconv display-referred path, `lws=10000` (γ=1.702 per fmtconv formula, darker SDR result; demonstrates the effect of the `lws` parameter). *(Rendered to 8-bit for display purposes.)*¶

../../_images/colorbarsuhd_pqtosdr.png — ColorBarsUHD mode=1 (PQ narrow) converted to SDR/BT.709 using fmtconv display-referred path (raw mapping without tone mapping). *(Rendered to 8-bit for display purposes.)*¶

The six example images above are generated by the following script. ImageWriter writes frames 0–5 as PNG files to the pictures/ subfolder. The fmtconv lws parameter on the first HLG transfer is the only lw-family parameter with any effect: it sets the HLG system gamma (γ=1.2 at lws=1000, the BT.2100 reference). All lw parameters on PQ transfers and on any non-first fmtconv transfer are silently ignored.

src_hlg       = ColorBarsUHD(width=320, height=180, pixel_type="RGBP10", mode=0)
src_pq_narrow = ColorBarsUHD(width=320, height=180, pixel_type="RGBP10", mode=1)
src_pq_full   = ColorBarsUHD(width=320, height=180, pixel_type="RGBP10", mode=2)

# HLG → SDR, lws=1000 → γ=1.2 (reference 1000 cd/m² display)
src_hlg.ConvertBits(32, fulld=true)
fmtc_transfer(transs="hlg", transd="linear", sceneref=false,
    \ fulls=true, fulld=true, lws=1000)
fmtc_primaries(prims="2020", primd="709")
fmtc_transfer(transs="linear", transd="1886", fulls=true, fulld=true)
sdr_hlg = last.ConvertBits(10, fulld=false)

# HLG → SDR, lws=10000 → γ=1.702 (fmtconv formula; darker; shows lws effect)
src_hlg.ConvertBits(32, fulld=true)
fmtc_transfer(transs="hlg", transd="linear", sceneref=false,
    \ fulls=true, fulld=true, lws=10000)
fmtc_primaries(prims="2020", primd="709")
fmtc_transfer(transs="linear", transd="1886", fulls=true, fulld=true)
sdr_hlg_mod = last.ConvertBits(10, fulld=false)

# PQ narrow → SDR (display-referred, raw mapping; all lw ignored)
src_pq_narrow.ConvertBits(32, fulld=true)
fmtc_transfer(transs="2084", transd="linear", sceneref=false,
    \ fulls=true, fulld=true)
fmtc_primaries(prims="2020", primd="709")
fmtc_transfer(transs="linear", transd="1886", fulls=true, fulld=true)
sdr_pq = last.ConvertBits(10, fulld=false)

function ToRGB8(clip c) { return c.ConvertBits(8).ConvertToRGB24() }

Interleave(
    \ ToRGB8(src_hlg), ToRGB8(src_pq_narrow), ToRGB8(src_pq_full),
    \ ToRGB8(sdr_hlg), ToRGB8(sdr_hlg_mod),   ToRGB8(sdr_pq))
Trim(0, 5).ImageWriter("pictures/colorbarsuhd_", type="png")

Syntax and Parameters

ColorBarsUHD (int "width", int "height", string "pixel_type",
              bool "staticframes", int "mode")

width, height

Set the size of the returned clip. The height defaults to width × 2160 / 3840, preserving the standard 16:9 aspect ratio. Standard resolutions supported by the ITU reference geometry are 1920×1080 (2K), 3840×2160 (4K) and 7680×4320 (8K), but any width is accepted and the geometry is scaled accordingly.

Default: 3840, 2160

pixel_type

Set the colour format of the returned clip. The primary intended formats are:

"RGBP10" — planar RGB 10-bit (default, matches ITU reference)
"RGBP12" — planar RGB 12-bit

The following formats are also supported:

Integer: "RGBP8", "RGBP14", "RGBP16"
Float: "RGBPS" (32-bit float)
YUV 4:4:4: "YUV444P8", "YUV444P10", "YUV444P12", "YUV444P14", "YUV444P16", "YUV444PS"

YUV output uses the BT.2020 NCL matrix (consistent with BT.2111 recommendations) BT.2020 CL (constant luminance) is intentionally not used, as CL encoding computes luma from linear RGB rather than gamma-encoded RGB.

Default: "RGBP10"

staticframes

If set to false, all frames are generated individually. If true (default), a single static frame is computed once and served for every frame request.

Default: true

mode

Selects the signal variant as defined in BT.2111-3:

0 — HLG narrow range (Table 2). Primary colour bars at 75% (code 721 at 10-bit). Transfer: ARIB B67 (HLG). Range: limited (64–940 at 10-bit) for 8-16 bits. 32-bit float output is always full-range.
1 — PQ narrow range (Table 3). Primary colour bars at 58% (code 573 at 10-bit), 100% top row. Transfer: ST 2084 (PQ). Range: limited (64–940 at 10-bit) for 8-16 bits. 32-bit float output is always full-range.
2 — PQ full range (Table 4). Primary colour bars at 58% (code 594 at 10-bit), 100% top row. Transfer: ST 2084 (PQ). Range: full (0–1023 at 10-bit).

Default: 0 (HLG narrow range)

Frame Properties¶

ColorBarsUHD sets the following frame properties on the output clip, allowing downstream filters such as z_ConvertFormat (zimg/avsresize) to auto-detect the source colour space via use_props=1:

Property	mode=0 (HLG)	mode=1 (PQ narrow)	mode=2 (PQ full)
`_Matrix`	0 (RGB) for RGB output 9 (BT2020_NCL) for YUV	0 (RGB) for RGB output 9 (BT2020_NCL) for YUV	0 (RGB) for RGB output 9 (BT2020_NCL) for YUV
`_Transfer`	18 (ARIB_B67 / HLG)	16 (ST2084 / PQ)	16 (ST2084 / PQ)
`_Primaries`	9 (BT.2020)	9 (BT.2020)	9 (BT.2020)
`_ColorRange`	1 (limited) 8-16 bits 0 (full) 32-bit float	1 (limited) 8-16 bits 0 (full) 32-bit float	0 (full)

Note

AviSynth uses an inverted convention for _ColorRange relative to ITU-T H.265: AVS_COLORRANGE_LIMITED = 1 and AVS_COLORRANGE_FULL = 0. This is the opposite of the AVS_RANGE_* convention. Inspecting _ColorRange with propShow() will show 1 for limited-range output (modes 0 and 1) and 0 for full-range output (mode 2).

Pattern Layout¶

The spatial layout follows BT.2111-3 Fig. 1 and is identical across all three modes. The pattern consists of five horizontal rows:

Row 1 (b/12 height) — 100% luminance colour bars
Row 2 (b/2 height) — 75% (HLG) or 58% (PQ) primary colour bars
Row 3 (b/12 height) — grey staircase (12 steps)
Row 4 (b/12 height) — grey ramp (continuous)
Row 5 (b/4 height) — bottom section: BT.709-equivalent bars, PLUGE, and black/white/black patches

The 2K reference width is 1920 pixels. All geometry is linearly scaled for other resolutions. At 10-bit the ramp endpoints and stair steps match the ITU table note values exactly at all standard resolutions (2K/4K/8K) and at both 10-bit and 12-bit.

Signal Levels¶

All signal levels are taken directly from the BT.2111-3 integer code value tables (Tables 2, 3 and 4 for 10-bit; §5 specifies 12-bit as 10-bit left-shifted by 2 for narrow range). Full-range signal levels at 12-bit have no equivalent bit-shift relationship defined in the standard; the 12-bit PQ full-range tables are defined distinctly in their own right. For HLG narrow (mode 0) and PQ narrow (mode 1), conversion to other bit depths uses the same left-shift for integer formats and a normalised float representation for 32-bit float output. For PQ full-range (mode 2), 10-bit and 12-bit levels are each defined by their own tables; other bit depths are derived from the 10-bit reference values scaled according to full-range rules rather than a simple bit-shift. The BT.709-equivalent colour bars embedded in Row 5 were derived by ITU per BT.2111-3 Attachment 1 using the HLG OETF and the BT.2087 limited-precision matrix (709→2020 direction) — these are the values as they appear in the standard, not computed by ColorBarsUHD. This means ±1–6 code differences from conversion tools are expected and normal — see the HLG-to-SDR conversion notes below.

HLG-to-SDR Conversion: Tool Comparison and Accuracy Notes¶

This section documents the behaviour of three widely used conversion tools — fmtconv, zimg/avsresize and HDRTools — when converting the ColorBarsUHD HLG test pattern to SDR/BT.709, and explains the sources of discrepancy between them and the ITU-R BT.2111-3 Table 7 reference values.

Understanding these differences is important for anyone using ColorBarsUHD as a validation source for HLG conversion pipelines. This investigation took considerable effort and is documented here in full so that future users do not need to repeat it.

Both scene referred and display referred paths were tested. HDRTools supports only display-referred.

Reference: ITU-R BT.2111-3 Table 7¶

ITU-R BT.2111-3 Table 7 provides reference output signal levels for both scene-referred (Fig. 10) and display-referred (Fig. 12) HLG-to-SDR conversion of the BT.709-equivalent colour bars in Row 5.

The ITU reference tool used the following conditions:

BT.2020-to-BT.709 primaries matrix derived from the normative 3-decimal chromaticity coordinates specified in BT.2020 (R: 0.708/0.292, G: 0.170/0.797, B: 0.131/0.046).
The embedded BT.709-equivalent bars were generated using the BT.2087 limited-precision matrix (4 decimal places, 709→2020 direction). ITU itself notes that ±1–6 code differences from tools using higher-precision matrices are therefore expected.
The display-referred path (Fig. 12) appears to have used a per-channel OOTF rather than the luminance-weighted OOTF defined in BT.2100, based on backward calculation from the reference values.
The output re-encoding used the BT.1886 EOTF inverse (pure power x^(1/2.4)), not the BT.709 camera OETF.
PLUGE reference values are not provided in Table 7. The PLUGE levels are inherently display- and OOTF-dependent, sitting at the edge of visibility where different OOTF implementations diverge most. No single correct output value exists for PLUGE after display-referred conversion.

Comparison of HDR source rendering by different tools¶

The BT.2020-to-BT.709 colour primaries matrix is derived from the source and destination chromaticity coordinates (xy values). The ITU-R BT.2020 document specifies these to 3 decimal places as the normative values. However, the underlying spectral locus primaries can be expressed to higher precision (5 decimal places), and some tools use these higher-precision values internally.

This distinction matters critically at gamut boundary colours such as the BT.709-equivalent Magenta bar, where the green channel value after matrix conversion is essentially zero — sitting right on the boundary between a marginally positive and a marginally negative number.

With 3-decimal normative coordinates (zimg default, ITU tool):

After BT.2020→BT.709 matrix, Magenta green channel: +0.000184
→ rec_1886_inverse_eotf(0.000184) = 0.02775
→ output code ≈ 88 = 0x58  (matches ITU Table 7)

With 5-decimal high-precision coordinates (fmtconv original default):

After BT.2020→BT.709 matrix, Magenta green channel: −0.00018
→ clipped to 0.0 (no negative output)
→ output code = 64 = 0x40  (diverges from ITU Table 7)

A difference of only 0.00036 in the intermediate green value — caused solely by chromaticity coordinate precision — determines whether green survives or is clipped. This is not a bug in either tool; it reflects a genuine ambiguity at the gamut boundary caused by the choice of source chromaticity precision.

Output Transfer Function: BT.709 OETF vs BT.1886 EOTF Inverse¶

A significant source of discrepancy is the choice of output re-encoding transfer function for display-referred conversion.

The BT.709 standard defines two related but distinct curves:

BT.709 OETF (camera curve): encodes scene linear light to signal. Contains a linear segment 4.5x for values below 0.018054. Correct for scene-referred encoding.
BT.1886 EOTF inverse: the mathematical inverse of the display transfer function x^(1/2.4). This is what actual displays implement, and is the correct re-encoding function for display-referred content.

zimg automatically applies the correct substitution based on the scene_referred parameter:

// From zimg transfer.cpp:
case TransferCharacteristics::REC_709:
    func.to_gamma = scene_referred ? rec_709_oetf
                                   : rec_1886_inverse_eotf;

fmtconv requires the user to explicitly request BT.1886:

# WRONG for display-referred (uses camera OETF with linear segment):
fmtc_transfer(transs="linear", transd="709", ...)

# CORRECT for display-referred (uses display EOTF inverse):
fmtc_transfer(transs="linear", transd="1886", ...)

The difference is most pronounced at near-zero signal levels such as the green channel of the BT.709-equivalent Magenta bar (~0.00018 linear). In the linear toe of the BT.709 OETF (4.5 × 0.00018 = 0.00083), the result differs dramatically from the BT.1886 path (0.000184^(1/2.4) = 0.02775), producing output code 65 vs 88. The ITU reference agrees with the BT.1886 result (code 89 = 0x59).

For scene-referred conversion, transd="709" remains correct since scene-referred encoding uses the camera OETF by definition.

fmtconv: Use Full Float Workflow¶

fmtconv operates internally at 16-bit integer precision unless the source clip is 32-bit float. Different filters are used for each steps. When intermediate results are 16-bit integer, two quantisation steps occur — after fmtc_transfer and after fmtc_primaries — which corrupt near-zero boundary values:

Marginally negative values (e.g. green = −0.00018) may be clipped to zero at the wrong stage, changing the final result.
Marginally positive values near zero lose precision and may round incorrectly.
Rounding errors accumulate differently across bars, producing results inconsistent with the full-float path and the ITU reference.

Always pre-convert to 32-bit float before HLG conversion in fmtconv. When converting a limited-range source to 32-bit float, use ConvertBits(32, fulld=true) — the fulld=true parameter is required so that fmtconv receives the pixel values in true full range (0.0–1.0) as expected for float input:

src = ColorBarsUHD(width=1920, height=1080, pixel_type="RGBP10",
    \              mode=0)
src = src.ConvertBits(32, fulld=true)  # limited-to-float, full range
sdr = src
    \ .fmtc_transfer(transs="hlg", transd="linear",
        \ sceneref=false, fulls=true, fulld=true, lws=1000, lwd=100)
    \ .fmtc_primaries(prims="2020", primd="709")
    \ .fmtc_transfer(transs="linear", transd="1886",
        \ fulls=true, fulld=false, lw=100)
    \ .ConvertBits(10)

The 16-bit intermediate workflow introduces ±1–10 code differences on boundary colours compared to the full-float path and should be avoided for validation work.

fmtconv HLG System Gamma: Formula and lws Values¶

The lws parameter on the first fmtc_transfer call controls the HLG system gamma applied during display-referred conversion. The gamma determines how the HLG signal is mapped to the SDR output luminance range.

Measured values via FmtcTransferDbg (fmtconv debug output):

lws = 100  cd/m²:  γ = 0.846,  scale_s = 3.076
lws = 1000 cd/m²:  γ = 1.200,  scale_s = 4.922  (BT.2100 reference)
lws = 10000 cd/m²: γ = 1.702,  scale_s = 9.592

The formula fmtconv uses (empirically derived from the debug output) is:

γ = 1.2^(1 + ln(Lw/1000) / 1.2)
  equivalently: γ = 1.2 × (Lw/1000)^(ln(1.2)/1.2)
                  = 1.2 × (Lw/1000)^0.15182

This differs from both formulas in BT.2100:

BT.2100 main:      γ = 1.2 + 0.42 × log₁₀(Lw/1000)  → 1.620 at 10000 cd/m²
BT.2100 footnote:  γ = 1.2 × 1.111^log₁₀(Lw/1000)   → 1.333 at 10000 cd/m²
fmtconv:           γ = 1.2 × (Lw/1000)^0.15182        → 1.702 at 10000 cd/m²

At lws=1000 all three formulas agree (γ=1.2), so the choice of formula only matters when using non-reference peak luminance values. For ColorBarsUHD documentation and validation purposes, lws=1000 (γ=1.2) is the BT.2100 reference and is the correct value for a 1000 cd/m² HLG display.

zimg/avsresize: Required Patch for Scene-Referred HLG¶

As of 20260319, during the ColorBardsUHD validation work, it turned out, that zimg's scene-referred HLG path (Z_ConvertFormat scene_referred=true) contained a normalisation error. The linear scene output was scaled by a hardcoded factor of 12.0 rather than by the correct factor 1.0 / OETF⁻¹(0.75).

This caused the HLG reference white (E'=0.75) to map to scene-linear 3.18 rather than 1.0, severely overflowing the BT.709 output range and producing clipped 0x3FF values for most colour bars.

The fix in transfer.cpp, select_transfer_function:

// BEFORE (wrong): normalises to scene linear 1/12, not ref white
func.to_linear_scale = scene_referred ? 12.0f : ...

// AFTER:
if (scene_referred) {
  // Normalise so that OETF^-1(0.75) = 1.0 (reference white = 1.0 in scene linear).
  // The original 12.0 normalised to scene linear 1/12, not to reference white.
  const float ref_white_scene = (std::exp((0.75f - ARIB_B67_C) / ARIB_B67_A) + ARIB_B67_B) / 12.0f; // ~0.26496..
  func.to_linear_scale = 1.0f / ref_white_scene;
  func.to_gamma_scale = ref_white_scene;
} else ...

After this patch, zimg scene-referred results match ITU Table 7 within ±1 code across all bars and agree closely with fmtconv.

Additionally, approximate_gamma=false is mandatory for zimg display-referred HLG conversion. The default approximate_gamma=true applies a simplified per-channel power function instead of the correct luminance-weighted OOTF, producing severely wrong results for chromatic colours:

# approximate_gamma=false is mandatory — default true is wrong
# for display-referred HLG
sdr_zimg = z_ConvertFormat(src, pixel_type="RGBP10",
    \ colorspace_op="auto:auto:auto:auto=>rgb:709:709:l",
    \ nominal_luminance=203.15,
    \ use_props=1,
    \ approximate_gamma=false,
    \ scene_referred=false)

zimg/avsresize: use full-range RGBP output¶

zimg does not clamp the float intermediate to the limited-range maximum before converting to integer RGBP output. Requesting =>rgb:709:709:l produces values up to code 1023 (full-range maximum) even for signal that should be capped at code 940 (limited-range white). This causes all colour vectors to appear at inflated radii on the vectorscope.

Always request full-range output explicitly (=>rgb:709:709:f) and then rescale to limited range via ConvertBits if needed:

# Wrong: limited-range output clamp is broken in zimg
sdr = z_ConvertFormat(src, pixel_type="RGBP10",
    \ colorspace_op="auto:auto:auto:auto=>rgb:709:709:l", ...)

# Correct: request full range, rescale afterwards if needed
sdr = z_ConvertFormat(src, pixel_type="RGBP10",
    \ colorspace_op="auto:auto:auto:auto=>rgb:709:709:f", ...)
sdr_limited = sdr.ConvertBits(10, fulld=false)

This applies to PQ sources. For HLG display-referred paths the 75% bar values are safely within BT.709 range so the bug has negligible impact.

HDRTools: pre-convert input to 16-bit full range¶

HDRTools builds its internal lookupL_32 transfer-function table in full-range normalised units (0.0–1.0), but indexes it using limited-range code values that have been bit-shifted (code × 64 instead of code × 65535/1023). The mismatch scales by up to ±0.3%, but because the HLG and PQ OETFs are strongly nonlinear, the error produces different scaling per channel depending on signal level. On the vectorscope this appears as a "star scatter": the three bars of each hue group land at different radii instead of the same radius.

Workaround: pre-convert the limited-range 10-bit source to 16-bit full range before passing it to HDRTools. The Coeff_Y=1.0 path that HDRTools uses for full-range input normalises correctly by dividing by 65535.0:

srcyuv.ConvertBits(16, fulld=true)
ConvertYUVtoXYZ(..., fullrange=true)   # fullrange=true is also required

HDRTools: output scale clipping at FF00 instead of FFFF¶

In the unpatched HDRTools source, ConvertXYZtoYUV caps the output at 255 << 8 = 0xFF00 = 65280 instead of 0xFFFF = 65535. At 10-bit limited range, 75% white should convert to code 940 (0x3AC), but the capped maximum produces code 937 instead. At 100% white the discrepancy is larger.

This bug is fixed in the patched source (data.Max_Y = vmax - 1 for full range, matching the 0..65535 range of ConvertYUVtoXYZ). Applying the ConvertBits(16, fulld=true) workaround above also avoids the issue on the input side; the output-side fix is required for correct 100% white reproduction.

zimg/avsresize problems: YUV444P10 output artifacts with PQ¶

At final RGB stage R=7.8 G=0 B=0 is converted then to YUV. Fully saturated Red -> Yellow, Magenta and blue are affected as well.

OOTF Method: Luminance-Weighted vs Per-Channel¶

BT.2100 defines the HLG OOTF as a luminance-weighted operation: the system gamma is applied to the luminance Y only, then each RGB channel is scaled proportionally, preserving chromaticity.

fmtconv implements this correctly via its GammaY module, applying gamma to luminance Y and scaling RGB channels proportionally.

zimg (with approximate_gamma=false) applies the inverse OETF first then scales each channel by Ys^(gamma-1) — equivalent to the luminance-weighted OOTF, producing results within ±1–2 codes of ITU.

The ITU Table 7 display-referred values appear to have been generated with a per-channel OOTF (gamma applied independently to each channel), which is technically non-compliant with BT.2100. For neutral colours (R=G=B) all methods are identical. For chromatic colours, fmtconv diverges from ITU by up to ±10 codes while zimg diverges by ±1–2 codes. Neither is incorrect — they implement different valid interpretations of the OOTF, with fmtconv's luminance-weighted approach being more faithful to BT.2100.

Near-black behaviour differs more sharply between tools because the HLG OETF uses a square root curve below E'=0.5, making the OOTF highly nonlinear in that region. PLUGE levels (−2%, +2%, +4%) are affected most — fmtconv's approach (OETF⁻¹ first, then scale) is more physically correct near black, while zimg's inside-OETF scaling causes larger deviations in the toe region. Since ITU Table 7 does not provide PLUGE reference values, no tool-independent ground truth exists for PLUGE after display-referred conversion.

Measurement Results Summary¶

All measurements on BT.709-equivalent colour bars, 10-bit limited range output. Input: ColorBarsUHD mode=0 (HLG narrow range), RGBP10. Values are R/G/B in hexadecimal. Y=Yellow, CY=Cyan, G=Green, Mt=Magenta, R=Red, B=Blue.

Display-referred conversion (ITU Fig. 12):

Tool / Configuration               |  Y        |  CY       |  G       |  Mt       |  R       |  B
-----------------------------------|-----------|-----------|----------|-----------|----------|----------
ITU Table 7 reference              | 3A5 3A6 40| 40 39C 39A| 7C 393 63| 356 59 355| 343 40 40| 5D 40 300
fmtconv 5-digit 2020 primaries     | 3A5 3A7 40| 62 39C 39A| 78 393 69| 356 40 355| 342 40 4C| 75 40 300
fmtconv 3-digit 2020 primaries     | 3A5 3A7 40| 40 39C 39A| 7B 393 64| 356 58 355| 343 40 40| 5B 40 300
zimg (approximate_gamma=false)     | 3A5 3A7 40| 40 39C 39A| 7B 393 64| 356 58 355| 343 40 40| 5B 40 300
HDRTools (full-range workaround)   | 3A5 3A7 40| 40 39C 39A| 7B 393 64| 356 58 355| 343 40 40| 5B 40 300

HDRTools with the full-range pre-conversion workaround matches zimg and fmtconv (3-digit 2020) exactly. Without it, all bars show systematically higher code values due to the input normalisation mismatch described above.

Scene-referred conversion (ITU Fig. 10):

Tool / Configuration               |  Y        |  CY       |  G       |  Mt       |  R       |  B
-----------------------------------|-----------|-----------|----------|-----------|----------|----------
ITU Table 7 reference              | 3AB 3AC 40| 40 3AC 3AB| 47 3AB 42| 3AC 41 3AC| 3AC 40 40| 42 40 3AC
fmtconv                            | 3AA 3AC 40| 42 3AC 3AB| 45 3AB 43| 3AC 40 3AC| 3AC 40 40| 48 40 3AC
zimg patched                       | 3AB 3AC 40| 40 3AD 3AB| 46 3AB 42| 3AD 41 3AC| 3AD 40 40| 42 40 3AC

PLUGE signal levels after HLG→SDR conversion (no ITU reference values):

#                  -2%         +2%         +4%       75% white
# fmtc scene    40 40 40    41 42 42    47 48 48    3AC 3AC 3AC
# zimg scene    40 40 40    42 42 42    48 48 48    3AC 3AC 3AC
# fmtc display  40 40 40    40 40 40    42 42 42    3AC 3AC 3AC
# zimg display  40 40 40    52 52 52    67 67 67    3AC 3AC 3AC

For scene-referred conversion, fmtconv and patched zimg agree on PLUGE values (−2%=40, +2%≈42, +4%≈48) with only ±1 code difference — within normal rounding tolerance.

For display-referred conversion, zimg gives significantly higher PLUGE values (+2%=52 vs fmtconv 40, +4%=67 vs fmtconv 42). This is caused by zimg's inside-OETF approximation in AribB67InverseOperationC: it prescales E' by Ys^0.2 before applying OETF^-1 rather than after. In the near-black square root region of the HLG OETF (E' ≤ 0.5) this algebraic shortcut accumulates larger errors than in mid-tones or highlights — precisely where the PLUGE signal lives.

fmtconv applies OETF^-1 first then scales by Ys^0.2, correctly separating the electro-optical inverse from the OOTF power law. This is more physically correct for near-black display-referred content.

Since ITU-R BT.2111-3 Table 7 provides no PLUGE reference values, neither approach can be validated against the standard. For PLUGE calibration purposes, fmtconv display-referred is the more trustworthy reference.

HDRTools display-referred PLUGE values are not available — HDRTools applies its own near-black rounding which has not been measured against this pattern.

HLG→SDR Conversion Scripts¶

The scripts below convert ColorBarsUHD mode=0 (HLG) to SDR/BT.709 and display the result on a vectorscope. targets100=true draws the 100% amplitude target boxes: the 75% HLG primary bars exceed BT.709 range and should clip exactly to these targets.

Parameter notes for HLG conversion:

fmtc_use_float = true — pre-converts to 32-bit float before fmtconv. Required for accurate results; see fmtconv float workflow.
lws=1000 on the first fmtc_transfer — sets the HLG system gamma. At lws=1000, γ=1.2 (the BT.2100 reference for a 1000 cd/m² display). fmtconv uses γ = 1.2 × (Lw/1000)^0.15182, which differs from the BT.2100 main formula at non-reference values; see the gamma formula section above. This is the only lw-family parameter with any effect in the HLG chain.
sceneref=true — ITU Fig. 10 path: inverse OETF only, no OOTF. Re-encodes to transd="709" (camera OETF).
sceneref=false — ITU Fig. 12 path: inverse OETF + luminance-weighted OOTF. Re-encodes to transd="1886" (BT.1886 EOTF inverse, correct for display-referred).
nominal_luminance=203.15 — anchors HLG reference white (diffuse white ≈ 203.152 cd/m² at 1000 cd/m² peak) to SDR white.
approximate_gamma=false — mandatory for zimg display-referred HLG; selects the correct luminance-weighted OOTF path.
scene_referred=false / true — zimg equivalent of sceneref.
HDRTools full-range workaround: srcyuv.ConvertBits(16, fulld=true) + fullrange=true — required to avoid the lookupL_32 normalisation error; see HDRTools limited-range input.
Coeff=49.2242 — derived from 1.0 / (OETF⁻¹(0.75)^1.2 × 0.1) = 1.0 / 0.0203152, mapping the HDRTools-normalised display reference white to SDR 1.0.

width = 480
fmtc_use_float = true

srcrgb = ColorBarsUHD(width=width, pixel_type="RGBP10",    mode=0)
srcyuv = ColorBarsUHD(width=width, pixel_type="YUV444P10", mode=0)

src = fmtc_use_float ? srcrgb.ConvertBits(32, fulld=true) : srcrgb
use_float = fmtc_use_float

# ── zimg/avsresize scene-referred (ITU Fig.10) ───────────────────────
# Requires patched zimg with corrected HLG scene normalisation.
srcrgb
sdr_zimg_scene = z_ConvertFormat(pixel_type="RGBP10",
    \ colorspace_op="auto:auto:auto:auto=>rgb:709:709:f",
    \ nominal_luminance=203.15, use_props=1, scene_referred=true)

# ── zimg/avsresize display-referred (ITU Fig.12) ─────────────────────
# approximate_gamma=false is mandatory — default true is wrong for HLG.
srcrgb
sdr_zimg_disp = z_ConvertFormat(pixel_type="RGBP10",
    \ colorspace_op="auto:auto:auto:auto=>rgb:709:709:l",
    \ nominal_luminance=203.15, use_props=1,
    \ approximate_gamma=false, scene_referred=false)

# ── fmtconv scene-referred (ITU Fig.10) ──────────────────────────────
src
fmtc_transfer(transs="hlg", transd="linear", sceneref=true,
    \ fulls=use_float ? true : false, fulld=true, lws=1000)
fmtc_primaries(prims="2020", primd="709")
fmtc_transfer(transs="linear", transd="709",
    \ fulls=true, fulld=use_float ? true : false)
sdr_fmtc_scene = last.ConvertBits(10, fulld=false)

# ── fmtconv display-referred (ITU Fig.12) ────────────────────────────
src
fmtc_transfer(transs="hlg", transd="linear", sceneref=false,
    \ fulls=use_float ? true : false, fulld=true, lws=1000)
fmtc_primaries(prims="2020", primd="709")
fmtc_transfer(transs="linear", transd="1886",
    \ fulls=true, fulld=use_float ? true : false)
sdr_fmtc_display = last.ConvertBits(10, fulld=false)

# ── HDRTools display-referred (ITU Fig.12) ───────────────────────────
# Only display-referred is supported. Pre-convert to 16-bit full range
# to avoid the lookupL_32 normalisation error (see HDRTools notes above).
srcyuv
ConvertBits(16, fulld=true)
ConvertYUVtoXYZ(Color=0, HDRMode=1, HLGLw=1000,
    \ OOTF=false, EOTF=true, OutputMode=2, fullrange=true)
ConvertXYZ_Scale_HDRtoSDR(Coeff_X=49.2242, Coeff_Y=49.2242, Coeff_Z=49.2242)
ConvertXYZtoYUV(Color=2, pColor=0, OOTF=false, EOTF=true, fullrange=true)
sdr_jpsdr_disp = last.ConvertBits(10, fulld=false)

# ── Vectorscope comparison ────────────────────────────────────────────
# targets100=true: 100% amplitude boxes validate that 75% HLG primary
# bars (which overflow BT.709) clip to exactly 100% SDR amplitude.
# Scene-referred: all same-hued bars should land spot-on the 100% targets.
# Display-referred: scatter between same-hued bars is physically correct —
# the luminance-weighted OOTF scales each bar differently by luminance.
StackVertical(
    \ sdr_zimg_scene.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets100=true)
        \.Subtitle("HLG scene-referred zimg/avsresize"),
    \ sdr_fmtc_scene.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets100=true)
        \.Subtitle("HLG scene-referred fmtconv"),
    \ sdr_zimg_disp.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets100=true)
        \.Subtitle("HLG display-referred zimg/avsresize"),
    \ sdr_fmtc_display.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets100=true)
        \.Subtitle("HLG display-referred fmtconv"),
    \ sdr_jpsdr_disp.Histogram("color", bits=8, targets100=true)
        \.Subtitle("HLG display-referred HDRTools")
\ )

PQ→SDR Conversion Scripts¶

The scripts below convert ColorBarsUHD mode=1 (PQ narrow) to SDR/BT.709. targets=true draws 75% amplitude boxes (58% PQ bars should land here for scene-referred); targets100=true draws 100% boxes (100% top-row bars).

Parameter notes for PQ conversion:

lws, lwd, lw in fmtconv — all ignored for PQ. PQ is an absolute transfer function (1.0 = 10000 cd/m²); fmtconv always divides by 10000 regardless of any lw parameter.
sceneref=true — applies PQ EOTF⁻¹ + OOTF⁻¹ → scene-linear. After scene-referred conversion, 58% PQ primary bars land on the same 75% BT.709 vectorscope targets as HLG scene-referred (same scene light level by ITU design). Re-encodes to transd="709".
sceneref=false — PQ EOTF only → display-linear. Re-encodes to transd="1886".
nominal_luminance=203.1521 — anchors PQ diffuse white (≈ 203.152 cd/m², the shared HDR reference white per BT.2408) to SDR white for both scene and display-referred paths.
=>rgb:709:709:f — use full-range zimg RGBP output; limited-range zimg RGBP output is broken for PQ (see zimg limited-range note above).
HDRTools: HDRMode=0 for PQ (vs HDRMode=1 for HLG). Same full-range workaround required. Coeff=49.2242 identical derivation as HLG.

width = 480
fmtc_use_float = true

src    = ColorBarsUHD(width=width, pixel_type="RGBP10",    mode=1)
srcyuv = ColorBarsUHD(width=width, pixel_type="YUV444P10", mode=1)

src = fmtc_use_float ? src.ConvertBits(32, fulld=true) : src
use_float = fmtc_use_float

# ── zimg/avsresize scene-referred ─────────────────────────────────────
# Use :f (full range) output — zimg limited-range RGBP output is broken.
sdr_zimg_scene = z_ConvertFormat(src, pixel_type="RGBP10",
    \ colorspace_op="auto:auto:auto:auto=>rgb:709:709:f",
    \ nominal_luminance=203.1521, use_props=1, scene_referred=true)

# ── zimg/avsresize display-referred ───────────────────────────────────
sdr_zimg_disp = z_ConvertFormat(src, pixel_type="RGBP10",
    \ colorspace_op="auto:auto:auto:auto=>rgb:709:709:f",
    \ nominal_luminance=203.1521, use_props=1,
    \ approximate_gamma=false, scene_referred=false)

# ── fmtconv scene-referred ────────────────────────────────────────────
# lws is ignored for PQ — no lw parameter needed anywhere in the PQ chain.
src
fmtc_transfer(transs="2084", transd="linear", sceneref=true,
    \ fulls=use_float ? true : false, fulld=true)
fmtc_primaries(prims="2020", primd="709")
fmtc_transfer(transs="linear", transd="709",
    \ fulls=true, fulld=use_float ? true : false)
sdr_fmtc_scene = last.ConvertBits(10, fulld=false)

# ── fmtconv display-referred ──────────────────────────────────────────
src
fmtc_transfer(transs="2084", transd="linear", sceneref=false,
    \ fulls=use_float ? true : false, fulld=true)
fmtc_primaries(prims="2020", primd="709")
fmtc_transfer(transs="linear", transd="1886",
    \ fulls=true, fulld=use_float ? true : false)
sdr_fmtc_display = last.ConvertBits(10, fulld=false)

# ── HDRTools display-referred ─────────────────────────────────────────
# HDRMode=0 for PQ. Same full-range workaround as HLG.
srcyuv
ConvertBits(16, fulld=true)
ConvertYUVtoXYZ(Color=0, HDRMode=0,
    \ OOTF=false, EOTF=true, OutputMode=2, fullrange=true)
ConvertXYZ_Scale_HDRtoSDR(Coeff_X=49.2242, Coeff_Y=49.2242, Coeff_Z=49.2242)
ConvertXYZtoYUV(Color=2, pColor=0, OOTF=false, EOTF=true, fullrange=true)
sdr_jpsdr_disp = last.ConvertBits(10, fulld=false)

# ── Vectorscope comparison ────────────────────────────────────────────
# Scene-referred: targets=true → 58% PQ bars land on 75% targets;
#                 targets100=true → 100% top-row bars clip to 100%.
# Display-referred: targets=false (75% targets not hit by 58% PQ);
#                   targets100=true → only 100% bars clip to 100%.
StackVertical(
    \ sdr_zimg_scene.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets=true, targets100=true)
        \.Subtitle("PQ scene-referred zimg/avsresize"),
    \ sdr_fmtc_scene.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets=true, targets100=true)
        \.Subtitle("PQ scene-referred fmtconv"),
    \ sdr_zimg_disp.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets=false, targets100=true)
        \.Subtitle("PQ display-referred zimg/avsresize"),
    \ sdr_fmtc_display.ConvertToYUV444(matrix="709:l")
        \.Histogram("color", bits=8, targets=false, targets100=true)
        \.Subtitle("PQ display-referred fmtconv"),
    \ sdr_jpsdr_disp.Histogram("color", bits=8, targets=false, targets100=true)
        \.Subtitle("PQ display-referred HDRTools")
\ )

Warning

When using fmtconv for PQ→SDR conversion, the 16-bit integer intermediate workflow produces significantly degraded results compared to the 32-bit float workflow. The difference is most visible on the vectorscope for Cyan and Green bars, where the integer workflow causes the colour vectors to land at approximately 50% of their correct radius — far from the expected 75% target positions. This is caused by two quantisation steps (after fmtc_transfer and after fmtc_primaries) corrupting near-zero and near-gamut-boundary values in the intermediate 16-bit representation.

Always use the full 32-bit float workflow for fmtconv PQ conversion:

src = src.ConvertBits(32, fulld=true)  # promote to float first

The 32-bit float workflow produces results matching zimg within ±1-2 codes across all bars including Cyan and Green, and all six colour vectors land correctly on the 75% vectorscope targets after scene-referred conversion.

../../_images/colorbarsuhd_pq_scene_fmtconv.png — PQ scene-referred — fmtconv (32-bit float).¶

../../_images/colorbarsuhd_pq_scene_fmtconv_integer.png — PQ scene-referred — fmtconv (16-bit integer; Cyan/Green at ~50% radius).¶

../../_images/colorbarsuhd_pq_scene_avsresize.png — PQ scene-referred — zimg/avsresize (full-range RGBP output).¶

../../_images/colorbarsuhd_pq_scene_avsresize_limited.png — PQ scene-referred — zimg/avsresize (limited-range RGBP output, broken).¶

../../_images/colorbarsuhd_pq_scene_avsresize_yuv.png — PQ scene-referred — zimg/avsresize YUV444P10 output (overflow artefacts on saturated primaries).¶

../../_images/colorbarsuhd_pq_display_fmtconv.png — PQ display-referred — fmtconv (32-bit float).¶

../../_images/colorbarsuhd_pq_display_avsresize.png — PQ display-referred — zimg/avsresize (full-range RGBP output).¶

../../_images/colorbarsuhd_pq_display_avsresize_limited.png — PQ display-referred — zimg/avsresize (limited-range RGBP output, broken).¶

../../_images/colorbarsuhd_pq_HDRTools_display_full.png — PQ display-referred — HDRTools (full-range 16-bit workaround).¶

../../_images/colorbarsuhd_pq_HDRTools_display_limited.png — PQ display-referred — HDRTools (limited-range input, broken).¶

HDR Reference White and the 203 cd/m² Value¶

Both PQ and HLG share a common HDR reference white — the luminance level that corresponds to diffuse white (a 100% reflectance card) in the HDR signal, and which is mapped to SDR white (1.0 = 100 cd/m²) during HDR-to-SDR conversion. The exact numeric value of this anchor depends on which standard is being consulted, and at what arithmetic precision the underlying formula is evaluated.

Base Formula (HLG)¶

The value originates from the HLG system. BT.2100-3 defines the HLG OETF inverse for signal levels E' >= 0.5 as:

E  = exp((E' - c) / a) / 12  +  b / 12

with constants (BT.2100-3, Note 5c):

a = 0.17883277
b = 1 - 4a         = 0.28466892
c = 0.5 - a*ln(4a) = 0.55991073

HLG reference white sits at signal level E' = 0.75. Display luminance follows from the HLG OOTF with system gamma γ = 1.2 (nominal 1000 cd/m² peak) and peak luminance L_W = 1000 cd/m²:

F_D = L_W * OETF^-1(0.75)^γ
    = 1000 * E^1.2

For PQ the value is adopted directly — BT.2408 designates the same luminance as the shared diffuse-white anchor for both systems. The oft-cited "58% PQ" figure is simply PQ_OETF(203 cd/m²) ≈ 0.5807 rounded; it is a consequence of the 203 cd/m² definition, not a definition in its own right.

Precision Variants¶

Evaluating the formula above at different arithmetic precisions, and rounding intermediate results as different standards and tools do, yields a family of slightly different values:

Source	F_D (cd/m²)	Coeff (10000/F_D)	Notes
BT.2408 (operational guideline)	203.0	49.2611	Rounded integer; human-readable mastering target
BT.2111-3 (HDR colour bars)	203.15	49.2247	Explicitly stated; more precise than BT.2408
Double precision (64-bit)	203.1521	49.2242	Full evaluation of BT.2100-3 constants
Float32 strict	203.1522	49.2242	Differs from double by < 0.0001 cd/m²; operationally identical

BT.2408 rounds to a whole number because a 0.15 nit difference is imperceptible in a mastering suite. BT.2111-3 uses 203.15 because its colour-bar definitions require the value to be mathematically consistent across PQ and HLG signal levels to more decimal places, but it does not carry the full precision of the BT.2100-3 formula. The remaining gap between 203.15 and 203.1521 (roughly 0.002 cd/m²) is below any meaningful display or grading threshold and arises purely from how many decimal places of the BT.2100-3 constants were retained before rounding.

Chosen Values For Test Scripts¶

Parameter	Value	Rationale
zimg / avsresize `nominal_luminance`	203.15	Matches the value explicitly stated in BT.2111-3. Provides more precision than the BT.2408 integer while resting on a direct standard reference rather than a computed approximation.
HDRTools `Coeff_X` / `Coeff_Y` / `Coeff_Z`	49.2242	Derived as `1.0 / 0.0203152` (= `10000 / 203.1521`), the double-precision result of the BT.2100-3 formula. Float32 evaluation yields the same four significant figures, so precision mode is not a factor.

Changelog¶

Version	Changes
AviSynth+ 3.7.6	Initial release of ColorBarsUHD. Implements ITU-R BT.2111-3 (05/2025) with three signal variants: HLG narrow range (mode=0), PQ narrow range (mode=1), and PQ full range (mode=2). Supports RGBP10/12 as primary formats plus 8/14/16-bit integer, 32-bit float, and YUV444 output. Height auto-derived from width. All frame properties set automatically.

References¶

Rec. ITU-R BT.2111-3: Reference service-level HDR colour bar test patterns.
Rec. ITU-R BT.2100: Image parameter values for high dynamic range television for use in production and international programme exchange.
Rec. ITU-R BT.2020: Parameter values for ultra-high definition television systems for production and international programme exchange.
Rec. ITU-R BT.1886: Reference electro-optical transfer function for flat panel displays used in HDTV studio production.
Rec. ITU-R BT.2087: Colour conversion from Recommendation ITU-R BT.709 to Recommendation ITU-R BT.2020.
Rec. ITU-R BT.814: Specifications of PLUGE test signals and alignment procedures for setting of brightness and contrast of displays.
fmtconv (AviSynth wiki): AviSynth wiki page for the fmtconv plugin.
fmtconv documentation: Full HTML reference documentation for fmtconv.
fmtconv releases (GitLab): fmtconv source releases on GitLab.
avsresize (AviSynth wiki): AviSynth wiki page for avsresize (zimg wrapper).
avsresize (Codeberg): avsresize source repository on Codeberg.
zimg (GitHub): zimg scaling and colour space conversion library.
HDRTools (AviSynth wiki): AviSynth wiki page for HDRTools (jpsdr).
HDRTools (GitHub): HDRTools source repository on GitHub.

$Date: 2026/03/28 00:00:00 $