Pentax shake reduction revisited

Update (April 18, 2010) Breaking News

The entire blog article may only apply to Pentax K-7 with firmware up to 1.00.02.xx with yet to be determined xx. Rüdiger from a German forum has done more measurements with 1.03 which seem to indicate this. I'll keep you updated.

End of Update.


This is a first for me. Because I am going to write about results obtained by others.

Nevertheless, I hope to be able to shed some new light onto an old question: How well does the Pentax shake reduction system work? The result may be surprising which is why I post this article.


1. Information sources

1.1 First and foremost, the admirable work by P. Smith for the Pentax K-7:
- Study of the Effectiveness of Shake Reduction in the Pentax K7
- Discussion of the above original work

1.2 Article by German magazines:
- ColorFoto 7/2008 "8 Bildstabilisatoren von 8 Herstellern"
- Pentax measurement chart contained therein
- ColorFoto 1/2010 "14 Bildstabilisatoren" (only available as print, pp.26-32).

1.3 Own work:
- Quick tests with my K-7
- Re-evaluation of data originally published by P.Smith
- Proposed mathematical model

Let me add that all data I am using (except my own quick tests) are based on a careful examination of edge blur widths (and their variation). Note that edge blur widths can be computed with high subpixel accuracy using the slanted edge method as all sources above do. They compare the shake (motion blur) with static blur caused by the sensor and lens too. Comparisons based on "percentage of useful shots" are not meaningful enough and therefore, haven't been used.

The work of P. Smith uses the Smith shake device aka as his body. The work of ColorFoto uses Steve aka Stabilization Evaluation Equipment which is an apparatus build exclusively for ColorFoto magazine. It was set to a mean shake frequency of 4 Hz and 0.2° amplitude. AFAIK, the shake isn't harmonic which is good.


2. Scope of the work

Aquiring a better understanding of the Pentax SR system. I am not in the boat to examine the 1/100s "SR bug" some report for the K-x and others deny. However, my article may help decide what is a bug and what isn't. My article will also help understand the performance differences of a sensor based system vs. an optical system.


3. A little background

Pentax uses sensor shift-based image stabilization (SR aka shake reduction). It is based on two (or three) angular velocity (gyro) sensors. More about the sensors:
- maRata Gyrostar ENC-03R

The measured angular velocities means that the body knows how the lens pointing direction is shaking and can shift the sensor to compensate. Unlike in-lens systems, it can even compensate for rotations around the axis which are not to be neglected. P. Smith has compiled a number of documents from the Pentax patent application:
- Pentax patents collected by P. Smith

Vendors with sensor-shift based image stabilization include Olympus, Pentax and Sony. Vendors with lens-tilt based image stabilization include Nikon, Canon and Sigma. A few lenses with lens-based stabilization for Pentax exist from Sigma. All systems are actively powered.

It is commonly accepted that neither system is superior to the other. I'll spend a few words on this later. No existing system works in the macro range. Canon has filed a patent requiring additional sensors to address this.


4. A fresh look at existing data


© 2010: measurement data: P. Smith; chart: F. Lumo.

This plot shows the blur width (in pixels) due to shake induced motion blur as a function of exposure time (in milli seconds; e.g., 1/125s = 8ms). The data is taken from the work by P. Smith as cited above. The red curve above is without shake reduction, the green curve is with shake reduction enabled. The thin lines denote upper and lower error margins (based on standard deviation and N=10 sample size). The dashed lines denote a fitted linear line thru the origin.

The camera used (Pentax K-7) has 5 µm pixels and the lens (Sigma 50/2.8 Macro) has 50 mm focal length.


This plot is the same as above with both axes in logarithmic scale. The green dashed line shows a linear line thru zero blur at 44 ms.

It turns out that all data by P. Smith are (within margins of statistical and systematic errors) compatible with the following formula (dotted lines in the above log-log plot):

b = a f |t - t0|

where b be the blur width (e.g., in µm),
a and t0 are constants,
and f be the focal length (e.g., in mm)
and t be the exposure time (e.g., in ms).

and where values are as follows:

SR OFF:
t0 = 0
a = 1 / (280 s)
(of course, a as above is a measurement of P. Smith's body tremor ;) )

SR ON:
t0 = 44 ms
a = 1 / (1200 s)

and b_SRON actually is the minimum of the above formula and b_SROFF. The crossover where b_SRON actually becomes b_SROFF is at t=8ms or 1/125s. For faster shutter speeds, the SR system has no effect (at 50mm focal speed).

The standard deviation of blur width is about the same size as the blur width itself, for both SR on and off.

This corresponds to an advantage of 2.1 stops within a nice range and actually better (~4 stops) around 1/20s - 1/25s. Persons with stronger tremor may see a better reduction.

The nice things about this formula is that we can compute the range of permissable shutter speeds, given a blur width and focal length.


5. Claim

The Pentax formula above holds true for all focal lengths.


6. Backing it up

Wait a second! If true, this claim means that the Pentax SR mechanism isn't able to help aquiring tac-sharp images with long focal lengths! Because below 1/125s, SR basically won't help anymore. It does help aquiring accepable images at maybe 1/50s and 200mm. But not tac-sharp at maybe 1/150s and 200mm. This may then require 1/400s actually, where SR on or off wouldn't matter anyway.

Because this claim is not to be made light-heartedly, I will use more sources to confirm it.

First, my own informal tests involving a visual inspection of images taken with a 300mm lens, at 1/320s, 1/160s, 1/100s, 1/25s, SR ON and OFF: the blur doesn't seem to depend on SR on or off with 1/320s, 1/160s, 1/100s. Blur was less at 1/25s with SR on but still a little bit more than at 1/160s with SR on or off.

Because this quick test isn't academic enough, I consult two additional sources: The ColorFoto tests from 2008 (K20D) and 2010 (K-7). The former measurement chart is online and I try to embedd it here (if it doesn't display, follow the link in the sources section):

© 2008 ColorFoto

We need to look at the second chart here, taken at 130mm and 1/125s. The red bar is with SR off and the dark blue bar to the right is with SR on. As you can see, both bars are roughly of same height, i.e., ColorFoto found SR ineffective at 130mm and 1/125s with the K20D. They actually found blur to be less at 1/15s than at 1/125s...

Now in 2010, I have the paper source for the same test with the K-7 and DA60-250 at 130mm at my disposition. Result: SR on (compared to SR off) has a positive effect of only 10% at 1/200s and maybe 20% at 1/100s. In a range of 1/200s to 1/13s, it remains at about 1 to 1.5 pixels as opposed to 0.5 pixels with tripod. Which is excellent at 1/13s but not so good at 1/200s. Their same curve at 23mm focal length reveals contant, tripod-like blur between 1/30s and 1/8s and even at 1s, only 2px blur. Their result is a little bit less irritating than the earlier K20D result in so far as shorter exposure times didn't lead to more blur.

These are two independent measurements basically coming to the same result: The Pentax SR is designed "to kick in" at exposures longer than about 1/50s.

This leads me to make my claim above.


7. Compared to the competition

In their 2010 study, ColorFoto compared the following SR systems, both at 35mm equivalent and 200mm equivalent focal lengths (FT and APS-C sensors).

35mm: (improvement in stops vs. 1/30s):
Nikon 18-200 VR II: 5
Olympus E3: 5
Panasonic GH1: 3
Sigma 18-50: 3
Pentax K-7: 3 (*)
Canon 18-135: 1
Sony A380: 1
Tamron 17-50: 0

200mm:
Olympus E3: 3
Panasonic GH1: 2
Canon 18-135: 1
Nikon 18-200 VR II: 1
Tamron 18-270: 1
Sony 70-300: 1
Canon 100: 0
Nikon 70-200 VR: 0
Sigma 70-300: 0
Pentax K-7: 0 (*)

(*) I define the number of stops improvement by the time where blur becomes more than 120% compared to a tripod shot, using the 1/focal-s rule to define the 0 stop point. The K-7 had more published shake without SR than the others which can only mean that the higher resolution wasn't corrected for. So, it was ok to add 1 stop to Pentax results (and avoid a -1 stop improvement listing ;) ).

So, all vendors have a common problem already at 100mm (FT) and 130mm (APS-C) focal lengths. At the long end, the best and the worst result are from sensor-shift based systems. At the wide end, they are mixed as well. So, differences are always due to the particular implementation details and not the principle as such.

Looking at results in more detail, I can see the "kick in effect" for the following systems: Tamron 18-270, Nikon 70-200 VR, Canon 100, Sigma 70-300 and Pentax K-7. So, it isn't a system-immanent effect.


8. Pentax SR usage guide

One can compile a usage guide of good exposure times based on the formula given above. This is possible because we can now assume that it holds true for all focal lengths.

The above is a 2D plot of ranges of good combinations of exposure time and focal length. The bright green (tack-sharp) represents 1 µm extra blur due to shake or better (0.2 pixels), the red (blurry) represents 20 µm blur or worse (4 pixels). The two darker shades of green (sharp and soft) represent degrees of blur, which are bearly or clearly noticeable at the 100% crop level.

The border between the two darker green regions represents the standard 135-format 1/f rule (1/(1.5*f) in APS-C land).

The blue or lilac region (blurred) represents a region where blur is obvious but not ruining the shot when looked at from the normal viewing distance: 20µm or 0.02mm is the traditional circle of confusion diameter for depth of field calculations.

One may think that the level of DoF-kind of sharpness be good enough. It depends on the subject. Because a crop from a shorter focal length would have done as well then. Sometimes, the longer focal length would still be the better choice because it collects more light (less noise than the crop) and allows for better focussing.

(Note: the chart and chart description was updated 2010, April 16.)


As can be seen, for focal lengths larger than 100mm, it is getting increasingly difficult or impossible to obtain the required sharpness from the SR mechanism and one has to use the good old rule of thumb. Nevertheless, if one shoots at 200mm and is accepting 1 pixel motion blur, then the avaible range is extended down from about 1/150s to 1/25s or 1/15s even, with the region around 1/100s to be avoided!

One may think that adding a tele lens from Sigma with lens-based stabilization could deliver more headroom for long range tele photo shots. In theory, this may be true. But it remains to be seen if the image stabilization mechanism made by Sigma can deliver for longer focal lengths. It may well be limited to the wide end as well. Additional tests would be required to answer this question.


9. Conclusion

Pentax delivers a capable shake reduction system able to provide up to 4 stops stabilization. However, it is designed to work best at exposure time around 1/20s and therefore, is most useful for normal and wide angle lenses used at low light or in video. Starting at around 100mm focal length, it is increasingly unlikely to see a positive effect from the SR system and beyond 200mm, the SR system cannot be used anymore to produce tac-shap images at lower than usual exposure times.

Olympus shows that this isn't a principle limitation of sensor-shift by delivering best stabilization for longer focal lengths (as far as I am aware of tests). So, there is hope that a future installment of the Pentax SR system is more useful for long focal lengths.

I call it "Tele-SR" and say to Pentax: I want it and I want it now :)


Thanks for stopping by.

LumoLabs: HowTo long range telephoto shots

It all started when I shot the sunset panorama below from one of the locations where I work. It shows a horizontal field of view comparable to a 60mm lens on a 35mm film camera. There is nothing exceptional about this panorama except maybe that it shows -- on the righthand side -- the Zugspitze which happens to be Germany's highest mountain.


The Zugspitze is 2962 m (or 9718 Ft) high and from the point where the photo was taken, exactly 83.39 km (or 52 miles) away. So, I thought it may be a good idea to crop into that image and look what guys are doing up there on mountain top ;)

Theoretically, such a crop should be feasible because the image actually was stitched from several images taken with the FA* 300mm f/4.5 lens on the Pentax K-7 each. So, a pixel corresponds to as little as 1.4 m up there on mountain top and this excellent lens clearly outresolves the sensor.

Below is what the crop (100% pixel level and corresponding to a 2000mm lens on 35mm film) looks like:


Really looks blurry as if it were out of focus or having motion blur. Actually, razor-sharp trees in 300 m distance point out that this may play a role as well. Because 300 m isn't within hyperfocal distance for 5µm at f/8. But as we'll see, we can actually ignore this little detail.

Lesson #1: Focus on something about 1-2 miles away (i.e., which is within hyperfocal distance for a 5µm circle of confusion) because infinity may be too blurry to focus at and more nearby objects may be, well too nearby.

As it turns out, the real problem actually is that large distance objects look blurry indeed (no wonder the auto focus didn't properly lock on them).

So, I ask myself the question how sharp to expect an object at a given distance to appear?

There is scientific literature about this but I couldn't find anything accessible to photographers. So, I decided to compile a little How To guide. Starting now ...


1. Possible optical resolutions for long range tele photographs taken in the atmosphere

Of course, photos taken outside the atmosphere aren't the most important category for most people reading this ;)

Another category are photos taken from the atmosphere into outer space (astro photography) and a common figure one is finding is to expect resolutions of up to 1 arcsec resolution but no better. In nights with very low atmospheric turbulence aka as excellent "Seeing". When the stars blink less than they usually do ;) This is related to the Fried parameter r0 which is about 5cm (sea level) to 20cm (in the mountains at a very good night) large. It isn't possible to achieve better resolution than with a diffraction-limited lens with diameter r0.

A lens with diameter 300mm/8 or 38mm (<r0) isn't limited by atmospheric turbulences. However, the turbulences vary at a time scale of t0 = 0.3 r0 / v_wind and with typical values of v_wind = 2 m/s (10 m above ground) we obtain t0 ~ 1/125s.

For anything slower than t0, we effectively smear out the turbulent perturbations and decrease the resolution.

Lesson #2: Shoot at 1/125s or less, even when on a tripod :)

Of course, I wasn't aware of this and used 1/25s. But as we shall see, this isn't a big problem either. Because for excellent results, we need extremely low noise (lower than at ISO 100) and will need a long effective exposure time.

One way would be to adaptively restore turbulent distortion using a parameterized grid and stacking many restored image frames. Which is nothing but applying adaptive optics.

Another and more practically feasible way is to accept the loss in resolution due to atmospheric turbulence. But how large is it?

Well, I managed to find a formula in the scientific literature and adapt it for an optical path with constant atmospheric conditions:

MTF_turbulence(f) = exp (-21.57 f^(5/3) lambda^(-1/3) Cn^2 L)

where:

MTF: Atmospheric modular transfer function
for turbulent distortions along a horizontal path [%].
f: angular spatial frequency [cycles/rad].
Cn^2: (refractive-index structure coefficient),
typically between 10^-15 and 10^-13 [m^(-2/3)].
lambda: wavelength e.g. 0.55 [µm].
L: pathlength e.g. 83.39 [km].

Source: R. E. Hufnagel and N. R. Stanley, "Modulation transfer function through turbulent media", J. Opt. Soc. Am. 54, 52–61 (1964).

A public online source (i.e., free of charge) discussing this formula is I. Dror and N. S. Kopeika, "Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere", (1995).

Be f = L / (2 x) where x is the size of the smallest resolved detail. Then I derive that the limiting resolving power (i.e. where MTF drops to 5.0%) is reached where

x = (L / L1)^1.6

where L1 = (1.633 * (Cn^2)^0.6 * lambda^-0.2)^(-5/8) is the distance where a 1m-sized detail can be resolved. Typical values are:

L1 = 50,000 [m^0.375] for weak turbulences (good seeing),
L1 = 20,000 [m^0.375] for normal turbulences,
L1 = 10,000 [m^0.375] for strong turbulences.

This formula as it stands is my own work and I hope it may be of good use for fellow photographers. The L1 values are slightly rounded (~10%) from the results using the typically rounded values for Cn^2 as given above. However, my table below uses L1 values as computed from the rounded Cn^2 values.

MTF jumps from 5% to about 40% for details twice as large (2x) and drops to below 0.01% for details half the size (x/2). So, there really isn't a reason to use more than one pixel per detail x and the maximum useful focal length can be computed from the above. The following table does so and assumes 5µm large pixels:

Distance [m]	max. focal [mm] (5 µm pixel)
Seeing:	good	normal	bad
1	171.410	43.056	10.815
2	113.088	28.406	7.135
5	65.261	16.393	4.118
10	43.056	10.815	2.717
20	28.406	7.135	1.792
50	16.393	4.118	1.034
100	10.815	2.717	682
200	7.135	1.792	450
500	4.118	1.034	260
1.000	2.717	682	171
2.000	1.792	450	113
5.000	1.034	260	65
10.000	682	171	43
20.000	450	113	28
50.000	260	65	16
100.000	171	43	11
200.000	113	28	7

This means that you don't have to care about atmospheric turbulence if you shoot shorter than 200 m only (assuming your longest lens is 500mm).

In all other cases, turbulence may be of concern. Typically, it may not be useful to shoot more far than 1 mile away. Because you would be tempted to use your longer than 500mm which then resolves worse than 500mm.

Lesson #3: Don't shoot your 20+ Gigapixel panorama at a day with just "normal" atmospheric turbulences.

Lesson #4: Wildlife photographers wanting to resolve 1mm at a bad Seeing condition day (like in Africa) either approach to at least 100m or use 1000mm f/22 (r0!) 1/250s (t0!) which applying the Sunny 16 rule, means a tripod and ISO 400...


2. Possible optical contrast for long range tele photographs taken in the atmosphere

So far, we looked at a loss of resolution due to atmospheric turbulences. While being the strongest enemy for astro photography (besides light pollution), it isn't for long range tele photographs. While crystal-clear days exist where it is possible to view 200 km far away (on a mountain), other days clearly exist where vision is limited to a few meters only (fog).

The normal is somewhere in between where aerosol particles (due to condensed water, smoke etc.) scatter light along its path thru the atmosphere and dramatically lower the MTF with distance. The effect is much more dependent on distance than on detail size which is why we tend to not even see the object at all. Nevertheless, if we see a distant object it may be at very low contrast only. Formulas exist for MTF due to atmospheric aerosol scattering. They only mean that the useful range of tele photo lenses is limited even more.

To make things more fun, turbulence and aerosol scattering counteract each other. Dry air normally means less aerosol scattering but more turbulences too due to the heat which dried the air in the first place.

Low contrast is of double concern. Because we may wish to reconstruct missing detail which is only possible for high signal to noise ratios.


3. Improving long range tele photographs

We will apply a three step procedure to improve our tele photographs. Note that this will only be applicable for static subjects, though.


Step 1: Improve the signal to noise ratio

I took 16 images and selected the best 10 of them. Then, I used PhotoAcute to align and stack them into a "superresolved" image with a signal to noise ratio corresponding to ISO 10:


If you click onto the photo and select "Original size", you'll see that the image is twice as large. But not sharp. PhotoAcute's superresolution technique actually works for images which are sharp in the first place. Here, we only used it to boost the signal to noise ratio. Parameters used are a Nikon D40 camera with Sigma 30mm/1.4 lens, a combination I found particlarly neutral, i.e., PhotoAcute doesn't try to deconvolve for lens aberrations too much ;)


Step 2: Sharpening

The next step is a restauration of image sharpness using a deconvolution technique. FocusMagic seems to deliver best results, even in the case here where the defocus' point spread function doesn't strictly apply.


The sharpness is clearly improved. I used a blur radius of 6 pixels (after scaling the image back to 50% size). And "Forensic" regularization, made feasible by the stacking in the prior step. There is a window reflecting the sun. And because being 83 km away, it should be a perfect point. The ring artefact is a sign that a different deconvolution kernel would have yielded better results.


Step 3: Contrast enhancement

The last step is boosting the contrast within the given area. All tone values are typically within just a small range and the first step is clipping. The remaining tone mapping may be done using a gamma correction and a dose of clarity.


This resulting image may not be the most beautiful image of the top of the Zugspitze mountain. Nevertheless, from 83 km away, it not only shows a radio emmitter pole which is 4 m wide at its base and 2 m wide at its middle portion. It even shows (in the background on the right side at a 45° angle) the steel cables of the Austrian side funicular. It doesn't resolve the individual cables. But imaging them at all from more than 50 miles away is ... well, interesting ;)

Lesson #5: Burst enough images to be able to boost contrast.

Lesson #6: Stock up on a bunch of capable post-processing tools.


I hope you enjoyed the read.


4. Links

1. I. Dror and N. S. Kopeika, "Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere", (1995)
   
2. PhotoAcute
   
3. FocusMagic
   

Lumolabs: Sensors of Nikon D700, D5000 and Pentax K-x

(Photo ©2009 Karsten Pawlik.)

After the interesting findings about the relatively good dynamic range properties of the Pentax K-x (cf. Lumolabs: Pentax K-x sensor quality), many have requested to publish a comparison with some other well known camera models.

Well, I am happy to announce that a great photographer and dear friend of mine, Karsten Pawlik (kafenio.org) shares my passion and we could spend some time in studio together in order to compile this comparison.

Most of the photos (e.g., all Nikon photos) presented in this article are © Karsten Pawlik. The opening photo shows two Pentax K-x with the gorgeous Pentax FA 31/1.8 Limited lens, in both black and silver color.

It is interesting to compare the K-x with these two cameras from Nikon for the following reasons:

1. Nikon D5000 and Pentax K-x may share the same Sony Exmor sensor which is supposed to be found in the Sony A500 too. (well, maybe not: DxO measures that the A500 has a different sensor)
2. Nikon D700 is a full frame camera and captures 1.2 stops more light than both the Nikon D5000 and Pentax K-x which are both APS-C only. It is interesting to see if this advantage shows in images.

1. ISO Noise


(please click on the photo above (and all others) for better readable versions)

The above chart summarizes the noise levels for 18% gray patches (2800 °K tungsten) at various values for ISO: 100, 1600 and 12800, measured as a signal to noise ratio (SNR [dB]). Please read Lumolabs: Welcome and testing methodology for details about how we measure these values. Towards the end of this article, you'll find links to all original test shots suitable for further examination.

Within this article, I will ignore the fact that the D5000 delivered the best SNR at ISO 100. AT ISO1600, we see the expected result: About 3dB or 1 f-stop (1EV) advantage for the full frame D700 with respect to both D5000 and K-x.

At ISO 12800, the K-x manages to match the result of the D700 while the D5000 behaves as expected. However, the SNR should decrease by at least 9dB when going from ISO 1600 to 12800 while it only decreases by only about 6dB for the K-x. This is a sign for raw file noise reduction at work for the Pentax and I believe that all SNR values for Pentax K-x should be reduced by 3dB for ISO values of 3200 or higher.

(Note: The D5000 has no native setting of ISO 12800. It was emulated using ISO 6400 and exposing like for ISO 12800, pushing 1 stop in postprocessing.)

In summary, we confirm the 1 stop advantage for the full frame sensor as far as high iso gray level noise is concerned.


2. Dynamic range

The situation turns out to be more complicated when we study the respective dynamic ranges. Let's start with the full SNR curves for all cameras.


Look first at the three red (D700 full frame), blue (D5000) and green (K-x) curves in the middle of the graph: These are the ISO 1600 curves for the three camera models and the red line lying above the others shows the full frame advantage we have been talking about above. The curves show how the signal-to-noise ratio decreases (relative noise increases) towards the shadows (the lower luminosities towards the left). At ISO 1600, the full frame advantage remains significant throughout all luminosities spanning 7 stops (1%). Note that the curves at ISO12800 may be "polluted" by noise reduction tricks for the APS-C sensors.

Most important for the determination of dynamic range are the SNR curves at lowest ISO (i.e., ISO 100). In order to measure deepest shadow noise, we made three shots at ISO100: normal, underexposed by -5EV and underexposed by -10EV! Patches from all three shots were analyzed to compile an SNR curve spanning 13 stops (down to 0.02% luminosity (which is RGB 0.05/255 and sRGB 0.6/255 aka perfect black)).

The surprising result is that at deepest shadows, the D5000 outperform the D700 by 2 dB and the K-x by even 5 dB. This should translate to about 0.5 EV more dynamic range for the D5000, and about 1.5 EV more dynamic range for the K-x, when compared to the D700. DxO does indeed confirm more dynamic range for the D5000 (12.5EV) compared to D700 (12.2EV). In combination, this is a confirmation for the "13EV or better" dynamic range claim I made in my earlier blog article.


3. Dynamic range (revisited)

I decided that this isn't the full story. Numeric results of measurements of noise are one thing. Plausibility checks are another.

(you must click the image and then select "O" (original size) to use this chart!)

The above chart contains various (small) noise patches from all cameras and ISO values. I even added some Pentax K-7 patches for comparison (Note: the K-7 has more pixels). Towards the end of this article, you'll find links to all original test shots suitable for further examination.

A quick examination of the patches at ISO 100 and -10EV shows that the D700 wins hands-down: better color accuracy, better readability of letters and better contrast. It sure looks slightly more busy (more noise) but the noise looks more fine grain too. More fine grain? Yes, the noise from the D5000 and K-x look coarser than the noise from the D700 or K-7. But noise should be statistically uncorrelated and look always fine grain (except for pattern noise).

Good detail note: all three cameras have no visible pattern noise.

Obviously, the sensor of the Nikon D5000 and Pentax K-x (and I guess it is the sensor rather than the firmware) plays some tricks with the signal in deepest shadows: there seems to be some sort of deep shadow noise reduction at work (like binning dark pixels) which leads to softer detail and a lower noise measurement.

Therefore, I conclude that the excellent dynamic range measurements of the D5000 and K-x are partly due to sophisticated signal processing, possibly on the sensor itself.

However, even taking this disclaimer into account, we can say that the deepest shadow reproduction of all three cameras play in one league: e.g., look at the 153 letters in the -10EV samples and compare to the K-7 (-9EV only) where the letters aren't legible anymore.

I conclude that by dynamic range, taking all information into account, the cameras rank as follows:

1. Nikon D700 (#3 by lab test)
2. Pentax K-x (#1 by lab test) and
   Nikon D5000 (#2 by lab test)

and are all very close.

The ISO12800 patches roughly confirm the numeric lab results. A K-x at ISO12800 and a K-7 at ISO6400 do roughly have the same noise while the K-7 keeps a slight resolution advantage even at such high ISO values.


4. Conclusion

Traditionaly, there is a one stop difference between full frame and APS-C. Temporarily, this sensor (Nikon D5000, Pentax K-x, supposed to be a Sony Exmor sensor) fills the gap (towards a Nikon D700) with respect to dynamic range while the difference remains with respect to high ISO noise.

This means that the D5000/K-x sensor has the same sensitivity to light as usual (as the D700) but has significantly reduced read-out noise.

The Pentax K-x may have a slight advantage over the Nikon D5000, esp. at very high ISO values. At the same time, this sensor (or firmware library) seems to include raw data alteration which makes the numerical analysis even more difficult, even when done in the DxO way. The time for true signal measurements has come, defining random noise as the sample variations of the signal and fixed pattern noise as the difference of the mean value with the ideal signal.

Lab tests (our own and the ones published by DxO) make the D5000/K-x have better dynamic range than the D700. But this is due to the limited testing methodology. D700 still has the better dynamic range, but by a small margin only.


5. Further reading

Access to full sample shot material:

• Pentax K-x test shots (full size)
• Nikon D700 test shots (full size)
• Nikon D5000 test shots (full size)
• Lumolabs: Welcome and testing methodology

Enjoy! :)

Lumolabs: Pentax K-x vs. K-7, sensor and video

Pentax has recently released a new SLR, the Pentax K-x. And while it is positioned at the entry-level market and very competitively priced, it is yet rumoured to have a very good noise performance.

After having done all my lab tests, I may say that the rumors are not true.

The truth is that the K-x may be the 35mm SLR camera which has the best high ISO noise and dynamic range performance to date. This isn't "very good". This is outstanding!

This is my concluding summary which is based on the following individual articles:

• Lumolabs: Pentax K-7 HD video quality
• Lumolabs: Pentax K-x HD video quality
• Lumolabs: Pentax K-7 sensor quality
• Lumolabs: Pentax K-x sensor quality

Noise and Dynamic Range comparison:

At the top of the article is a compilation of various gray sample patches for both cameras, for direct comparison. The patches are from linear raw files (cf. "further reading" at the end of the article).

The resulting 18% gray level chart is like this:


Signal to noise ratio of 18% gray luminosity and color temperature 2900°K (halogen tungsten). Using manufacturer ISO stops 100, 200, 400, 800, 1600, 3200, 6400, 12800. The interpretation of results is the same as for the corresponding graphs on dxomark.com. E.g., print-normalization is for 8 megapixels. The dotted lines indicate the slope for pure photon shot noise.

Obviously, the K-x has no true ISO 100 and both cameras reduce noise even in RAW at ISO 3200 and higher. The ISO sensitivity of the K-x seems to be slightly higher, like at ISO 100, true ISO were more like 87 for the K-7 (DxO's value for the K20D) and 105 for the K-x. However, the above curves have not been left/right-shifted to take this into account.

Gray level noise at ISO 1600/3200 for the K-x is about the same as at ISO 1000 for the K-7. While gray level noise at ISO 1600 and 3200 are about the same for the K-x, there is a minimal loss of resolution when looking at the pattern part in the full test charts. Nothing serious, though.


Signal to noise ratio (SNR) for the Pentax K-7 and K-x. Full measurement for various luminosities and ISO settings at color temperature 2900°K. Measurement similiar to dxomark.com. The dotted lines indicate the slope for pure photon shot noise. The flattening at 30% gray and brighter is believed to be due to systematic measurement errors like imperfect gray patches. The dashed curves for the K-x have been properly normalized to match the higher sensor resolution of the K-7.

The curve for K-7 only and test images are at:
Full SNR Pentax K-7

The curve for K-x only and test images are at:
Full SNR Pentax K-x

The K-x/ISO 200 and K-7/ISO 100 curves are almost identical down to 1% luminosity.

The full SNR graph clearly exhibits the true strength of the K-x sensor: it maintains the good SNR at low luminosity levels. This is an indication that the read-out noise from this sensor is very low.

Therefore, the K-x sensor outperforms the K-7 in low light situations whereas the K-7 outperforms the K-x in good light. This is further confirmed by the better resolution and more artifact-free images from the K-7.


Video:

The quality from HD video is very good. The resolution is as high as the 720p mode allows. It somewhat more moiré and color moiré artifacts than the K-7 and therefore, may not exactly match its analog and film-like quality in 720p mode. But it is very good nevertheless.


Conclusion:

The Pentax K-x has a sensor which rivals the best. That Pentax makes it available in the entry-level class is a good thing. On the other hand, the Pentax K-7 excells in many respects and even its noise performance isn't bad. It is in line with the rest of the competition which is beaten by the K-x in this respect now.


Pentax K-x: "Editor's choice" (entry level, available light)
Pentax K-7: "Editor's choice" (semi professional)



Further reading: Lumolabs testing methodology.

Lumolabs: Pentax K-x sensor quality

The Pentax K-x is an incredible machine for an entry level SLR. Here, I will look at the image quality which its sensor can produce.

In my lumolab testings, I will not report about ergonomics or lack of features etc. The internet is full of this easily obtained information and I will refrain from duplicating it here.


Test chart results:

The photo at the top of the article is an ISO test shot taken at ISO 1600 and color temperature 2900°K. It is a linearly converted RAW file (cf. "further reading" at the end of the article). Go to the gallery (click the image) to have a look at all test shots, available at original full size.


ISO resolution test chart using FA 31 Ltd. at f/4.5. The inner part is 4x. The Nyquist limit is at "7.1" in the inner part. Watch the original at 100% size.

The K-x resolves down to the Nyquist limit. However, it exhibits color moiré and false demosaicing at the limit frequency. The anti alias filter is very weak or absent as it allows for moiré down to three times the Nyquist limit. Color moiré is visible for textures at the Nyquist frequency.

E.g., note that the "7" patch has false demosaicing and strong color moiré. The same is visible from the zone plate chart. The K-7 doesn't show this in comparison.


Zone plate test chart using FA 31 Ltd. at f/4.5. The big circles have a resolution limit of 1280 LW/PH. The smaller ones are 2x and 4x. The 4x circles at above ~4000 LW/PH have uncolored printing moiré. The Nyquist limit is at 2848 LW/PH which is about 55% into the smallest circle. Watch the original at 100% size.

The zone plate chart of the K-x has false colors (fringing) already at half the Nyquist frequency and "green blobs" at three-quarter of the Nyquist frequency, followed by heavy color moiré at the Nyquist frequency exactly. The latter two effects are limited in spatial frequency space but the fringing is kind of disappointing.

While most testers will not notice the effect and welcome "the good resolving power of the K-x", which "leaves no resolution advantage to the K-7" (anticipated quotes from future pseudo tests), I personally would have preferred a stronger anti alias filter.


Numerical lab result:

The numerical evaluation of all noise charts (the full SNR plot) is as follows:


Signal to noise ratio (SNR) for the Pentax K-x. Full measurement for various luminosities and ISO settings at color temperature 2900°K. Measurement similiar to dxomark.com. The dotted lines indicate the slope for pure photon shot noise.

It is possible to derive both dynamic range and noise from the graph. If extrapolating the 0db point for ISO 100 at luminosity 0.01%, then the resulting dynamic range is 13.3 EV (print-normalized to 13.6 EV). E.g., DxO tests the print-normalized dynamic range of the K20D to be 11.05 EV and of the outstanding Nikon D3X to be 13.65. The flattening at 30% gray and brighter is believed to be due to systematic measurement errors like imperfect gray patches.

The theoretical photon noise separation between neighboring ISO lines is 3dB. There are three effects which can be observed:

- The SNR at ISO 100 is reduced for luminance levels above ~3% and drops to the ISO 200 values. A sign that ISO 100 is no native IO value for this sensor. On the other hand, it is exceptionally high for luminance levels below ~3%, with a boost more like ISO 75 than ISO 100.

- The ISO 3200 line is only 0.5 dB separated from the ISO 1600 line. DxO labs found that this is due to noise reduction applied to RAW data at ISO 3200 and higher. Without such noise reduction, the SNR would obviously be about 2.5 dB lower. This smoothing is even stronger than for the K-7.

Overall, the gray level noise (the SNR at luminosity 18.00%) is very close to the competition (worse at ISO 100, same at ISO 200 and better beyond) while the black level noise (the SNR at luminosity 0.10%) is very small. The ISO 1600 curve provides about the same black signal than ISO 100 pushed +4EV.

I have not measured SNR for luminance below 0.04%. But from extrapolation one may deduce that the K-x has a dynamic range of about 13.6 EV which would be even an excellent value for a full frame camera.


Update - The K-x "bump" at 2%, ISO 100 (2009, October 29):

Because of the importance of the ISO 100 SNR curve at low luminosities for the outstanding dynamic range claim made for the K-x, I have evaluated available testing material again, with special emphasis on this bump.


Signal to noise ratio (SNR) for the Pentax K-x. Full measurement for various luminosities and ISO 100 at color temperature 2900°K. Measurement similiar to dxomark.com. The dotted lines indicate the slope for pure photon shot noise.

This graph is meant to study the "bump" at about luminosity 2% in the ISO 100 curve of the full SNR graph (cf. above). The full 12 EV test chart is compiled from two parts: one exposed normally, another underexposed by 5 stops.

The above plot is a reexamination of both parts, now separately evaluated. There indeed is a discontinuous step (by +1.8 dB) when going from the normal to the -5EV curve which I cannot currently explain. The flattening of the brightest parts looks the same and could indeed be due to imperfect bright print patches. This would imply an underestimation of the "bump" by another 1.7 dB leading to a possible overall overestimation of SNR by +3.5 dB in the dark part.

Even taking this correction into account though, the above plot still confirms an extrapolated 0 dB SNR point at 0.01% luminosity. Therefore, the conclusions made in the other sesctions are not altered by this detail examination.

(end of update)


Conclusion:

- Resolution: Full Nyquist 12.2 Mpixel resolution, some moiré, some color moiré, some demosaicing artifacts. Very weak or absent anti alias filter.

- Noise: Gray level 40.0 dB at ISO 100, 31.6 dB at ISO 1600, dynamic range (print-normalized) >13 EV.

The image quality is good at low ISO values and very good if shadows are pushed-processed. It is outstanding at high ISO values and sets the bar for 2010. I haven't tested the Nikon D700 but from the known results, I say that the Pentax K-x is seriously challenging the D700 in terms of high ISO noise and dynamic range. With a much smaller body, a smaller sensor and a much smaller price tag ... and video ;)

I award the Pentax K-x the following title:

"Dynamic range champion 2009 in the 35 mm body class".



Further reading:
- Lumolabs: Pentax K-7 sensor quality
- Lumolabs testing methodology.