Log Gamma Profile

Definition

Log Gamma (English: Log Gamma Profile or Log Curve) is a nonlinear tone curve that converts camera raw data into a logarithmic color space. This maximizes the utilization of available bit depth by allocating more data to shadow details than to highlights.

The idea: Human perception is logarithmic, not linear. We perceive differences in dark areas more distinctly than in bright areas.

Perceptual Reality:
 Difference between 0% and 10% brightness: HUGELY perceptible
 Difference between 90% and 100% brightness: Barely perceptible

Log curve adapts to this:
 0-10% range: Allocates 30% of bit depth
 90-100% range: Allocates only 10% of bit depth
 
Result: Optimal information storage

Physical Principle

Linear vs. Log Tone Curves

LINEAR Tone Curve (like Rec.709 standard):

Brightness Output
 │
 │ ╱ Highlights clipping
 100%├─────────────────────────╱
 │ ╱
 │ ╱
 │ Midtones Range ╱
 │ ╱
 │ ╱
 │ Too Dark╱ 
 │ Shadows
 0%└──────────────────────────
 0% 100% Input Brightness

Problem: Highlights clipping frequent, shadows noisy

LOGARITHMIC Tone Curve (like ARRI LogC):

Brightness Output
 │
 │ ╱ Large "Headroom" for shadow details
 100%├──╱───────────────────────────
 │ ╱ 
 │╱ Shallow curve maximizes DR utilization
 │
 │ Gentle highlights (less clipping)
 │
 0% └──────────────────────────────
 0% 100% Input Brightness

Advantage: Even information distribution, no clipping

Mathematical Definition

LogC Formula (ARRI Standard):

For Input X (0 to 1):
 If X < 0:
 Y = cut / E 
 Else:
 Y = C * log₁₀(a*X + b) + d

Result: Log curve preserves information exponentially

Practically means:
 - Small input differences in shadows = Large output differences
 - Large input differences in highlights = Small output differences
 - Maximum utilization of 10-bit or 12-bit storage

Technical Specifications

Log Standards in Modern Cameras

Log vs. Rec.709 Tone Curve Comparison

Visual Difference at same exposure:

ARRI Alexa with Rec.709 Output (In-Camera):
 → Image looks immediately "colorful"
 → Colors are saturated
 → Highlights quickly overexposed
 → Shadows dark and noisy
 → Cannot be recovered in post

ARRI Alexa with LogC Output:
 → Image looks flat and desaturated
 → Colors very muted
 → All details visible (including highlights)
 → Shadows clean, very detailed
 → Must be calibrated in post with LUT

Post-Production Result:
 Log output with Rec.709 LUT:
 = Identical to in-camera Rec.709
 But with full grading flexibility + greater DR

Log in Practice

Production - Exposure Strategy

Log Exposure (Golden Rule):

"Expose for Highlights in Log"

Scenario: Interior with window backlight

Traditional Rec.709 Exposure:
 1. Meter on window
 2. Expose so window is not overexposed
 3. Interiors dark, but OK
 4. No post flexibility

Log Exposure:
 1. Meter on window
 2. Expose 1.5-2 stops over normal ("overexpose")
 3. Interiors bright, window also bright
 4. Monitor shows flat, overexposed image
 5. In post: LUT applied, perfectly balanced

Psychologically difficult:
 - Cinematographer sees bright, flat image
 - Must trust that post will be correct
 - Very different from "expose for highlights" in traditional film

Post-Production - Grading with Log

Standard Log Grading Workflow (DaVinci):

1. Import Material
 → LogC Files
 → Flat, desaturated appearance

2. Apply Viewing LUT
 → ARRI Rec.709 LUT
 → Image looks "normal"
 → But: Grading occurs in log-space

3. Grade in Log-Space
 → Shadows: Can lift +5-6 stops
 → Midtones: ±3 stops possible
 → Highlights: Can crush -2-3 stops
 → No posterization, clean tonality

4. Final Output
 → Rec.709 Master
 → ProRes 422 HQ (with LUT baked)
 → Or: DCP (Cinema Package)

Advantage: Shadow Recovery in Log

Scene: Night Exterior (slightly underexposed)

Traditional Rec.709:
 1. Underexposed capture
 2. Shadows lifted in post
 3. Result: Noisy, visible noise
 4. Grade limit: ~+0.5 stops lift possible

Log Workflow:
 1. Underexposed capture (looks very dark)
 2. Log-space: Shadows can be lifted +3-4 stops
 3. Result: Clean shadows with details
 4. Grade limit: +5-6 stops possible

Winner: Log provides dramatically more shadow flexibility

Different Log Standards

ARRI LogC (Industry Standard)

Specifications:
 - Developed by ARRI (2010)
 - Widely Adopted (ARRI, RED, Blackmagic, etc.)
 - Wide Color Gamut (Alexa Wide Gamut)
 - 10-12 Bit Depth
 - Preserves ~14 stops DR

Advantages:
 ✓ Industry standard (easiest to share)
 ✓ Excellent shadow recovery
 ✓ Compatible with many tools
 ✓ LUT-libraries widely available

Disadvantages:
 ✗ Proprietary (but de facto standard)
 ✗ Requires proper LUT for output

Sony S-Log3 (Extended DR)

Specifications:
 - Developed by Sony
 - Extendable to RAW-like DR
 - 10-Bit Depth
 - Proprietary color gamut (S-Gamut3)

Advantages:
 ✓ Very aggressively optimized for DR
 ✓ Good for high-contrast scenes
 ✓ Excellent highlight behavior

Disadvantages:
 ✗ Less LUT support than LogC
 ✗ Sony-specific color science
 ✗ Less compatibility with other cameras

RED REDlogFilm (Subtle Log)

Specifications:
 - RED's log implementation
 - Subtler than ARRI LogC (less flat)
 - 12-Bit native support
 - Proprietary color space

Advantages:
 ✓ Subtler tone curve (monitor-friendly)
 ✓ 12-Bit native (more bit depth)
 ✓ Good for cinema look

Disadvantages:
 ✗ RED-specific
 ✗ Less cross-compatibility
 ✗ Special REDcine-X tools required

Log + LUT Workflow

What is a LUT?

LUT = Look-Up Table

Function: Tone curve mapping

Input: Log value (0-1023 at 10-bit)
Output: Rec.709 value (0-1023 at 10-bit)

Example:
 Log 128 → Rec.709 210 (Brighter, more color)
 Log 256 → Rec.709 450
 Log 512 → Rec.709 800
 Log 1023 → Rec.709 1023

Result: Automatic conversion

ARRI Rec.709 LUT Example

Description: Standard ARRI LogC → Rec.709 conversion

Visual Transformation:
 Input (LogC): Flat, desaturated, low contrast
 Output (709): Normal, saturated, full contrast

File: ARRI_LogC_to_Rec709_v2.cube

Usage in DaVinci:
 1. Import LogC file
 2. Apply Node: 3D LUT "ARRI_LogC_to_Rec709"
 3. Image immediately looks calibrated
 4. Grade on top of it

Important: LUT is applied to monitoring,
 not to the raw data itself
 (Non-Destructive Grading)

Custom LUT Creation

Professional colorists often create custom LUTs:

Process:

1. Capture test chart (with log)
 → Gray balls at various light levels
 → Known color targets

2. Calibration
 → Export as DNG/OpenEXR
 → In post: Adjust to reference monitor
 → Grade the chart

3. Extract LUT
 → DaVinci / Baselight: Generate LUT
 → 3D LUT file is created
 → Can now be used for all footage

Result: Camera-specific, monitor-calibrated LUT

Log for Different Scene Types

1. High-Contrast Dramatic Scenes

Scenario: Film Noir interior (very high contrast)

Setup:
 - Strong key light (ISO 800)
 - Minimal fill light
 - Desired: Dramatic shadows

Log Advantage:
 - Can handle extreme contrast
 - Shadows retain details despite high contrast
 - Highlights retain color information
 
Result: Aggressive grading possible without quality loss

2. Daytime Exteriors

Scenario: Beach scene (extreme DR needed)

Challenge:
 - Very bright sky (overexposed easily)
 - Very dark shadows (underlit easily)
 - ~18 stops dynamic range to manage

Log Solution:
 - Expose for midvalues
 - Sky remains detailed in log
 - Shadow lift possible without noise
 
Result: Sky details + ground details possible

3. Indoor Night-Scenes

Scenario: Candlelit dinner (very dark)

Challenge:
 - Minimal light (candlelight only)
 - Shadows very dark, slightly noisy
 - But: Shadow details desired

Log Solution:
 - Aggressively overexpose in log
 - Monitor shows flat image
 - In post: Lift shadows without noise
 - Colors retain saturation

Result: Details in dark areas recoverable

Future Perspective

Log Evolution (2024-2030):

Current Standard:
 - ARRI LogC dominant
 - Sony S-Log3 growing
 - RED REDlogFilm niche

Future Trend:
 - More cameras adopting LogC-like profiles
 - Standardization on broader basis
 - AI-powered LUT generation
 - Cloud-based log-space grading

Prediction: Log becomes even more dominant, in-camera Rec.709 rarer

Practical Rule of Thumb

When to use Log?

Premium Production (Budget > €500k)?
 → Log mandatory for grading flexibility
 
Standard Production (Budget €100-500k)?
 → Log recommended, Rec.709 acceptable
 
Budget Production (< €100k)?
 → Rec.709 OK, log optional
 
Streaming / Social Media?
 → Rec.709 standard
 
DCP / Cinema Distribution?
 → Log standard (then mastered to Rec.709)

See Also

• Rec.709 – Standard output gamma
• Color Grading – Practical log usage
• LUT – Look-Up tables for log conversion
• ARRI LogC – Industry standard log
• Dynamic Range – Log preserves DR
• Raw Recording – Similar flexibility as log