Dear Sara,

the options mentioned by you mainly depend on what you want to obtain (see

below).

Independently from these options, ImageJ *will* transform images that have

side-lengths that are not a power of two. (Just try it!)

In general and classically, the Fourier-transformation of digitized images

with side-lengths that are not a power of two can be performed following two

approaches:

1. Using the DFT (Discrete Fourier Transformation)

This approach doesn't show the speed profit of the FFT-algorithm (Fast

Fourier Transformation). In other words, it is comparably slow. (The classic

FFT requires images with side-lengths that are a power of two.)

Here

<

https://sites.google.com/site/piotrwendykier/software/parallelfftj>

you find an implementation of the Fourier-transformation for ImageJ (plugin)

that uses the FFT-algorithm for images with side-lengths that are a power of

two and the DFT-algorithm for images with side-lengths that are not a power

of two.

2. Padding (embedding)

Images with side-lengths that are not a power of two are padded to the next

size with side-lengths that are a power of two. In other words, the small

image is embedded in an image support that has side-lengths that are a power

of two. This new support is previously filled with the mean value of the

small image.

As Michael pointed out already, this approach is used by ImageJ.*

(There is a different way of embedding that I prefer. It uses windowing and

embedding in an empty support. If you prefer this common approach, I can

provide a windowing plugin for ImageJ.)

The options you've mentioned (in fact their naming is far from reasonable):

1. FFT window

You get an 8bit result that is the Fourier-Power Spectrum with the spectral

values (gray-values) logarithmically scaled.

2. Raw power spectrum

You get a 32bit result that is the Fourier-Power Spectrum.

3. Fast Hartley Transform

For the time being, forget about this option.

4. Complex Fourier Transform

You get a 32bit stack (consisting of two slices) that represents the

complex-valued Fourier Transform. The first slice is the real part and the

second slice is the imaginary part of the complex-valued Fourier Transform.

The question remains, what you need for your purposes.

Please feel free to ask, if you have further questions.

Regards

Herbie

==========================================

*

ImageJ doesn't centrally embed the small image but puts it at the top left

of the new support. This doesn't make any difference for Power Spectra but

it does introduce a linear phase which has considerable impact on the

complex-valued Fourier spectrum.

If you need the complex-valued Fourier spectrum without this effect you need

to do the correct embedding yourself.

==========================================

Am 08.12.19 um 10:17 schrieb Sara_24:

> Hi Herbie,

>

> would you please tell me which of FFT options do the FFT of images of

> non-power of two size? I use Fiji and as FFT options it has only FFT

> Window,

> Raw power Spectrom, Fast Hartley transform, and complex Fourier transform.

> Which one do the FFT of images of non-power of two size?

>

> Best regards,

> Sara

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