----------- Your trusted source for independent sensor data- Photons to Photos------------------------ Last revised: 2021-03-27

# -------- Sensor Analysis Primer - Energy Spectra and Repeating Patterns

--------------------------------------------------------- By Bill Claff

### Introduction

In this article we will investigate how repeating patterns present in energy spectra.
The primary source of repeating patterns in image sensors is from unbalanced multi-channel readout and Phase Detect Auto Focus (PDAF) pixels.

### Random Banding

The electronics used to read out the value of the pixels can sometimes have a vertical or horizontal pattern.
Here is a random vertical pattern constructed by rearranging the DSNU data in a synthetically constructed frame:

The horizontal component of the Energy Spectrum shows large amounts of relatively even energy at many random frequencies.

Pixels might be read out in columns with groups of four column read out independently. Such a strategy would reduce total read time and improve frame rate.
But what if one of these four channels was not performing like the other three?

Now, rather than being random, the energy is organized into two peaks (I'm only showing the horizontal spectrum for clarity).
The primary peak has a wavelength of 4 and shows on the x-axis at 1/4 = 0.25 f/  fs
We also see peaks of equal height at multiples up the Nyquist limit; in this case 2/4 = 0.5; this is called a comb.

### Phase Detect Auto-Focus (PDAF)

Mirror-less cameras, as opposed to Single Lens Reflex (SLR) cameras, use PDAF pixels to achieve auto focus.
PDAF pixels behave differently than non-PDAF pixels and are often arranged in a regular pattern on the sensor.

What would it look like if every twelfth row were comprised of PDAF pixels?

As we might have expected we see 6 peaks with the primary peak at 1 / 12 = 0.825 (only vertical shown for clarity).

I did not choose this example at random. Let's look at the energy spectrum for a Nikon Z 6:

Except for some energy at 0 f / fs the vertical spectrum matches because this sensor must have PDAF pixels every 12th row on the sensor.

That energy at 0 results from the fact that the pixels on every 12th row alternate in how they differ. When we incorporate that into our synthetic frame we get:

### Phase Detect Auto-Focus (PDAF) More Complex Examples

When there is more than one frequency we get patterns of unequal heights that may even have gaps. Here is a rather complex example of the :
Here there are unequal pairs of pixels at a wavelength of 16 and within that 16 a pair with an offset of 4. This pattern occurs in both the horizontal and vertical directions.

And here is the energy spectrum for the Canon EOS 7D:

In the vertical direction we see unequal peeks from a pattern with a wavelength of 8 pixels that are pairs of unequally affected pixels.

### Where Did They Go?

Here is the energy spectrum for the Nikon Z 6 II:

The pattern exhibited by the Nikon Z 6 is gone. PDAF pixels don't always show as different; it depends on the sensor and firmware.

### A Final Example

Let's reexamine the energy spectrum for the Nikon Z6:

Looking closely at the horizontal we see that it drops from left-to-right which we recognize this as a low-pass filter.
We'll cover  that in more depth in Energy Spectra and Filtering.

### Conclusion

Depending on how PDAF pixels are treated they may show up as Fixed Pattern Noise (FPN) in the sensor data and an energy spectrum can help up determine their placement.
This may be interesting but unless the FPN is noticeable in our final images it is of no concern.