# Nikon 400mm f2.8 MTF Resolution

I did some resolution testing of the Nikon 400mm f/2.8 AI-S manual focus lens using both the Nikon D300 and the Nikon D3s camera bodies. I also evaluated the MTF of the above combinations using the Nikon TC-14E II 1.4x teleconverter. As expected this was the best lens that I have tested thus far. The resolution of the optics portion exceeds that of the camera sensors for the entire imaging systems, this was expected and was also true of the Nikon 70-200mm f/2.8 lens that I previously tested in past posts.

The minimum theoretical optical resolution of the glass can easily be calculated, for circular apertures the following formula can be used:

$\theta=1.22 \frac{\lambda}{d}$

Where $\theta$ is the minimum theoretical resolving angle in radians, $\lambda$ is the wavelength of light, and d is the diameter of the aperture. Using 656 nm for the wavelength of Hydrogen-Alpha (red) light the minimum resolving angle for the Nikon 400mm f/2.8 lens is approximately 1.2 arc-seconds of a degree. However the minimum width that can be resolved by any image sensor is determined by the lens focal length and the sensor pixel width. The minimum resolution is limited to two pixel widths since two separate pixels are required to differentiate the information, this also agrees with the Nyquist frequency minimum of two samples per cycle.

For the Nikon D3s the pixel size is 8.48 $\mu m$ and the D300 pixel size is 5.49 $\mu m$ thus the minimum resolving angles, with the 400mm lens, are 8.71 arc-seconds of a degree and 5.66 arc-seconds of a degree respectively. This correlates to the absolute minimum resolving angles as evaluated using the MTF test chart from Norman Koren MTF Tutorial. The MATLAB code, instructions for printing, photographing, data extraction, and MTF evaluation are also located at the above website link.

The best resolution was with the D300 since it has smaller pixels. Unlike the 70-200mm lens, the MTF curve is above the curve from the D3s in all areas. Remember that the 70-200mm lens the low spacial frequency was actually superior with the D3s and the crossover point was the 50% point. Here is the graph from the D300:

Here is the Chart for the Best resolution using the D3s at f/8.0. The D3s MTF results for f/11 and f/16 are nearly identical to f/8.0, while the D300 has a definite peak at f/11 and softens for apertures on either side:

Here is the actual photo of the Koren Chart for the D300, where the lines can no longer be differentiated the lines merge into grey, however prior to this point there is obvious aliasing occurring as can easily be seen by the colors and apparent chromatic aberrations occurring above the 1% MTF point or above 60-70 lp/mm:

Here is a crop of the aliasing area of the above image, note both chromatic aliasing as well as spacial aliasing by the checkerboard pattern, this may actually be picket-fencing which is actually the opposite of aliasing, instead of extraneous information occurring there may be masking of information due to the spacial frequency modulation caused by the anti-aliasing filter in the camera, also note the blueish sidebands surrounding the orange band:

The finest resolution of this lens occurred when the aperture on the lens was set to f/8.0 with the D3s and f/11.0 on the D300. When the Nikon TC-14E II teleconverter added the best settings were also the same on the lens, however, the actual effective aperture is reduced by one full stop or f/11.0 on the D3s and f/16.0 on the D300. There is pronounced resolution reduction with aperture settings fully open or closed. for example the worst resolution tested was with the D300 using the teleconverter, while the best resolution was with the D300 without the teleconverter. Here is the graph of the worst resolution tested:

Note that this curve corresponds approximately with the MTF curve of the Celestron 9.25 Edge HD optical tube. The worst possible Nikon 400mm scenario corresponds with the best case scenario using the Celestron tube. In other words astrophotography with the Nikon wide open, with a 1.4 teleconverter, at f/4.0 should produce similar resolution as using the Celestron tube in prime focus. Any other setting should produce superior results, and the Nikon is not in any way optimized for astrophotography.

Now for some actual photos of showing the performance of this lens. I found that removing all accessories from the Really Right Stuff (RSS) tripod was necessary, the Wimberly gimbal mount was attached directly to the top of the tripod, the ball mount and variable detent unit were removed. Otherwise there was too much vibration to be acceptable. I would also like to point out that the following images were taken during a heavy overcast and drizzly day.

The ISO was set to 1600, which is much higher than I like, and the shutter speeds were considerably longer than I would find acceptable for a long lens, even on a tripod. The effective focal length for the D300 are 600mm and 850mm using the teleconverter so the minimum shutter speeds would normally be 1/600s and 1/850s respectively, even on a tripod. The shutter speeds used were around 1/100s so I believe under the right conditions the following images could be much, much sharper.

Nikon D300 1/100s f/16 ISO 1600 1.4x teleconverter

Nikon D300 1/100s f/16 ISO 1600 1.4x teleconverter 100% crop

Nikon D300 1/250s f/11 ISO 1600

Nikon D300 1/250s f/11 ISO 1600 100% crop

From many other reviews of this lens it has been thoroughly documented that the 400mm f/2.8 lens is a bit soft at infinite focus as well as at minimum focus. The above images were captured very near the minimum focus of about 12 ft (3.6 m) and it can be plainly seen that the depth of field is extremely narrow at this short distance even though they were captured using a relatively small aperture which probably lea to the softness observed at minimum focus. I’m planning to do some additional tests to evaluate the sharpness at infinite focus sometime in the near future.

Because of this I had to use the handhold technique and even though I did use sandbags to reduce shutter vibrations in the lens the birds were nearly impossible to follow, I had to constantly adjust the focus to get the sharpest images. These buggers were quite hyper and a bit skittish since I had just put out the plate of seed for the first time earlier in the morning. The ability to successfully use this lens is quite a bit more challenging to master than the much lighter 70-200mm lens but I think that there is a whole lot of room for improvement that can be achieved with enough practice.

The one thing that I am now becoming aware of is that there must be a plan of attack thoroughly worked out prior to ever even thinking about using this lens. Unlike the 70-200mm lens, that can easily be hand-held or even carried around on a tripod or monopod and is a very good tool for simply cruising stealthily around and spontaneously exploring artistically ad hoc, this behemoth of a lens needs a definite plan. In other words hauling this big gun around is about as subtle as a Sherman tank in a china shop. Creeping up on any wildlife and setting up, without scaring the holy bejesus out of them, is a very difficult task indeed, I find that a lot of time and patience and a completely different strategy is absolutely necessary.