Horizontal scan instability

Visible effect

Successive camera-raster lines shift sideways

Horizontal edges no longer line up from one raster line to the next. Rows shift left or right by changing amounts, creating waviness, tearing, or a fine vibrating contour while vertical position remains stable.

This article isolates instability of the camera tube’s horizontal deflection and scan timing. Sync damage and time-base error introduced after the camera output can look similar, but belong to later representation, recording, or reproduction stages.

Physics

Horizontal deflection sets the position of each beam sweep

The electron beam reads the target sequentially. Variation in the horizontal deflection waveform or its oscillator changes where a sweep begins or how it traverses the target.

This page models that in-camera cause only. Loss of synchronization or time-base stability after the camera output is a separate downstream effect even when the visible row displacement is similar.

Mathematics

One horizontal offset per sampled line

A sinusoidal term creates correlated deflection waviness; signed noise adds local variation. Coefficient c_h is normalized to the vertical Nyquist limit: c_h = 1 alternates at the finest resolvable row frequency, while lower values produce broader bends. Frequency f is measured in cycles per second. Division by width W converts pixel amplitude to texture coordinates.

Shader

Height-scaled sine-plus-noise x remap

The mapping converts the normalized vertical-frequency coefficient to radians per row, advances temporal phase in cycles per second, calculates a horizontal displacement, then performs one inverse texture lookup.

// WHAT: Give each horizontal scan row a small sideways timing displacement.
// HOW: Combine a smooth vertical timing wave with row-held pseudorandom error,
// convert the requested pixel displacement to UV, and offset only source x.
// WHY: Horizontal timing error changes where a scan line begins; it does not
// bend individual objects continuously in both image directions.

// This sine hash is a visual random source, not an electronic noise equation.
float lineJitterHash(vec2 value) {
  return fract(sin(dot(value, vec2(12.9898, 78.233))) * 43758.5453);
}

vec2 horizontalLineJitter(
  vec2 uv,
  float time,
  float amplitudePx,
  float heightCoefficient,
  float rate,
  vec2 resolution,
  float imageHeight
) {
  // Quantize time so the random part is held instead of changing at every
  // sub-frame instant. band identifies the current destination scan row.
  float timeState = floor(time * max(1.0, rate));
  float rowIndex = floor(uv.y * max(1.0, resolution.y));

  // The smooth term makes low-frequency timing drift visible across rows.
  float periodicError = sin(
    3.14159265 * uv.y * imageHeight * heightCoefficient
      + 6.2831853 * time * rate
  );
  float randomError = lineJitterHash(vec2(rowIndex, timeState)) * 2.0 - 1.0;

  // 55/45 is a visual mixture of coherent drift and row-wise instability.
  float displacementPx = amplitudePx * (
    0.55 * periodicError + 0.45 * randomError
  );
  float displacementUv = displacementPx / max(1.0, resolution.x);

  return uv + vec2(displacementUv, 0.0);
}

Why these steps are here

1. Keep each target row vertically fixed.
2. Scale vertical phase from zero to the row-sampling Nyquist limit.
3. Renew the random deflection component at a bounded rate.
4. Convert pixel amplitude by output width.
5. Sample once at the shifted horizontal coordinate.

Notes

• This isolated model does not synthesize the actual deflection-coil current or oscillator circuit.
• Post-camera sync loss and time-base error require their own signal and buffering models.
• Large amplitudes are diagnostic rather than representative of a healthy camera.

References