SPECULATIONS ON THE MEGAPIXEL RACE OR "DO I NEED A + 32 MEGAPIXEL SENSOR?" By tjshot ([email protected])

This document is released under Creative Commons, CC BY-NC-SA license.

PART I – SENSOR AND PERFORMANCE

Recent announcements of 24 Mpxls APS-C and rumours of 36 Mpxls full frame sensors seem to have changed the scenario for digital enthusiasts, triggering opposite reactions: some of us are out of the skin to get the new babies (I'm among them) while others seem to question the effectiveness of such upgrades. We had similar doubts in the past when upgrading to higher density sensors and I've read many articles on the internet stating that you don't really need more than about 20 Mpxls full frame sensor (due to lens diffraction/aberration, sensor sampling performance etc.)

I hardly agree.

At the level of development we have reached today a small increase of pitch (effective sampling rate -> sharpness and resolution boost) in the sensor will induce a much higher (square growth law) megapixel count, thus requiring much larger in-camera buffer memory, faster data saving channels, more powerful computers etc.

At the same time noise control becomes increasingly difficult (square growth law) due to higher amplification of the signal needed to achieve the same ISO rating; on the other side smaller pitch sensors seem to produce a much more even and defined noise, partly counterbalancing the degradation in quality (think about the terrible "pepper" grain in Canon EOS 5D compared to the smoother Canon EOS 7D).

Many additional elements factor in, resulting in final image quality: A/D converter performance (12bit to 14bit seems to produce a very high boost in dynamic range, noise performance etc.), image processor, firmware etc.

We'll eventually get to a break-even point where the pros in increased sampling capability will match cons in noise and data rate, when it comes to final image quality and system usability.

I believe we have not reached this point yet.

My take on the matter is that for full frame bodies 32-36 Mpxls still makes sense in terms of performance improvement; 32 Mpxls is probably a better trade-off for the advanced user.

Lets consider a few factors.

1) Print size

With + 32 Mpxls it's possible to print to A3 + format (13x19 inches at + 350 dpi) without interpolation, which is the upper (easily usable) size limit for most advanced home printers (I'm assuming you are strict about colour management and want to directly print your work); if you regularly need more then you are probably a fashion pro and should consider (could afford) digital .

Interpolation to higher/lower sizes will always cause a loss of resolution and quality (upscaling being the worst case); I'd rather shoot with a resolution that exactly fits my highest requirements than having to pay (in terms of noise, image size and ... money) for an overhead that I'll hardly ever use.

2) Sharpness and Resolution That's where flame wars usually start on forums. The short story: 32-36 Mpxls on a Bayer matrix sensor is still "low enough" to squeeze significantly more information out of most of your . I see 65 Mpxls as the practical limit for an excellent prime at F 8. Probably no much sense in going over 50 Mpxls anyway (due to noise and dynamic range).

The long story: sharpness and resolution in a camera system depend mainly on lens performance and sensor sampling rate (pixel pitch in digital). Lenses for 35 mm usually reach top performance between F 5.6 and F 8; wider are affected by aberrations (colour fringes, halos, micro distortion like "coma" etc.), smaller apertures start to be affected by diffraction (an unavoidable physical property of light). I'll keep a qualitative approach and assume all the definitions and technicalities are known; many sources are available on the internet, Norman Koren's site being the one offering the most comprehensive - related background. A worth reading if you are math oriented. (Address: http://www.normankoren.com/Tutorials/MTF.html ) Diffraction is a property of light and sets the top obtainable performance of a lens for a given F-stop: for each F-stop and for a given wavelenght of light, there is a corresponding limiting resolution due to diffraction; a real lens can only perform lower than this limit, due to "losses" in the glass, by a margin depending on its quality. With actual technology it's relatively feasible to produce a nearly diffraction limited lens in the range F11 - F16; very few manufacturers seem to be interested in producing a commercially available lens (i.e. a profitable design) which is diffraction limited at wider F-stops (probably only Leica). Best lenses differ from average ones in their ability to control the aberrations that limit performance at wider apertures; to achieve a good result at extreme apertures (think of the best Leica, Canon, Zeiss fast primes with maximum F 1 - F 1.4 stop) without raising the price to unprofitable levels (and dropping light transmission), a few design compromises are often required, which involve some degradation of performance at more typical F-stops. In the following I'll propose some sharpness/resolution calculations, further developing some assumptions made in an article "Do sensors outresolve lenses?", published on Luminous Landscape that seems to have received some attention. (Address: http://www.luminous-landscape.com/tutorials/resolution.shtml ) Based on practical experience and some math speculation, a Bayer sensor, with proper sharpening procedures, is able of reproducing a signal with good accuracy when its sampling rate is at least 3 per cycle (1 cycle= 1 line pair). In the aforementioned article "required megapixels" calculations are based on a 2 pixels per line pair assumption, which implies a perfect alignment between signal (line pairs) and sample units (pixels) plus a sensor resolving straight down to its Nyquist limit; in practice the two will often be out of phase (misaligned) and anti alias filters, required for Bayer matrix technology, will degrade performance at higher frequencies (lp/mm), thus involving an oversampling requirement. 4 pixels per line pair seems to deliver optimal results with Bayer sensors. 3 is ok for most real scenarios, if proper sharpening is applied. About definition of "proper sharpening" there seem to be different opinions; I'm partial to integer radius values (mostly 1 and 2 radius) as I find they involve less software-induced aliasing. (Tech note: radius 1 sharpening is good when you have a sharp image to start with, as it generally boosts response at Nyquist frequency i.e. in the very high lp/mm near the resolution limit of the sensor(however it depends on sharpening algorithm used by software); radius 2 may be better for not-so sharp images, as it generally boosts response at lower frequencies (half Nyquist); for actual sensors with 4000 to 5000 dpi it falls in the 38 - 48 lp/mm range, corresponding to the combined MTF 50% value (perceived sharpness) of the sensor plus a good - excellent lens. In other words radius 2 sharpening, with a very good lens and a 21 + Mpxls sensor, lets you recover image information in the "lp/mm zone" where our eye-brain system perceives sharpness. Very effective.)

Following the 3 pixels per line pair sampling assumption, a 36 Mpxls Bayer matrix full frame sensor is able of registering most of the relevant information available from a nearly diffraction limited lens at F11: this is a pretty common performance both for modern primes and quality zoom lenses. In the following I'll propose some simulations obtained using real data from DXOmark site (Address: http://www.dxomark.com )and a Matlab function proposed by Norman Koren. To keep things simpler we'll consider only lens + camera, but printers are also involved in practice. As a reference for interpretation of following data, let's consider that: - The impression of sharpness is often related to the MTF 50% value of the imaging chain system: that's the frequency where contrast drops to half the value of the original target. In other words that's the value that suggests how much “WOW factor” the picture delivers due to sharpness. - The resolution is often related to the MTF 10% value of the imaging chain system: that's near the maximum perceivable detail a system is able of delivering before grain and noise start to prevail and mask information. You won't probably notice that detail unless enlarging the image very much (40 x with actual sensor pitch) on a monitor (or under a loupe film) and it would not be “clean enough” to be pleasant to the eye; so it's often assumed that it does not contribute much to the “WOW factor”. The more you'll enlarge, the more you'll be relying on low MTF information to build up your final, printed image. Just consider these as general guidelines, as perception and quality standards are also a subjective matter. Just to show the basics of the simulation, I'll start with a scenario that is well known to many users owning a current top DLSR: a “20 Mpxls range” full frame sensor (Canon 5D Mk II, but it can be extended to other top line bodies from Nikon and Sony). Values for such sensor with a perfect (diffraction limited) lens at different F- stop would be:

1 2 MTF values for a MTF values for a diffraction limited lens + 21 Mpxls diffraction limited lens Full Frame Sensor Wavelenght of light = Wavelenght of light = 0.00055 0.00055 No Sharpening Sharpened MTF MTF MTF MTF MTF 50% MTF 10% F-stop 50% 10% 50% 10% Sharpening Parameters (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm)

2.8 247 532 4 173 373 5.6 123 266 54 78 76 76 K=0.35 r=1 8 86 186 49 78 70 78 K=0.4 r=1 11 63 135 44 78 65 78 K=0.45 r=1 16 43 93 43 78 60 78 K=0.4 r=1 22 31 68 28 52 48 78 K=0.7 r=1

Where: Wavelenght of light is set about in the middle of the visible spectrum (Green- Yellow zone) as it's a common situation in daylight shooting; shifting towards blue will increase resolution, toward red will decrease it. K is the edge contrast boost ratio, usually set in % value by the slider in the sharpening software. R is the radius of sharpening, also set in the sharpening software. In previous table, sharpening parameters were set to what I consider the highest safe values still allowing a reasonable control of halos or artefacts. Values for F 2.8 and F 4 are not reported as they are of no practical use for comparison with real lenses. Let's see now how the sensor behaves with the simulation of a real excellent prime lens (think of a good sample of a Canon 85mm F 1.8 ; it's easy to match the simulation with real data from DXOmark site):

1 2 MTF values for excellent MTF values for for excellent real prime + 21 Mpxls real prime Full Frame Sensor Wavelenght of light = Wavelenght of light = 0.00055 0.00055 No Sharpening Sharpened MTF MTF MTF MTF MTF 50% MTF 10% F-stop 50% 10% 50% 10% Sharpening Parameters (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm)

2.8 37 75 63 78 K=0.5 r=1 4 37 75 63 78 K=0.5 r=1 5.6 65 195 41 78 65 78 K=0.45 r=1 8 53 159 37 75 63 78 K=0.5 r=1 11 45 135 34 70 61 78 K=0.55 r=1 16 38 91 31 62 55 78 K=0.6 r=1 22 28 68 25 52 49 78 K=0.7 r=1

For the simulated lens MTF 50% values were chosen to match the empirical data from the DXOmark site; MTF 10% were calculated using a simulation of “how the lens looses resolution” towards the higher lp/mm range(tech note: an MTF simulation curve with an order 2 rolloff was used for the F 5.6 – F11 range, i.e. the lens is performing well under the diffraction limit; an order 2.5 rolloff was used for F 16 – F22 as the lense behaves closer to the diffraction limited lens model in that range) A real lens does not reach the peak MTF 50% value of the ideal diffraction limited one but on the other side it looses resolving power more gradually towards the highest frequencies. Modern lens design for 35mm is optimized for performance at wider apertures: quality lenses will peak at F 5.6, a few even at F 4, and gradually loose performance at smaller apertures, where the quality is uniform across the whole field. At wider apertures and up to F 2.8 they are generally able to keep top performance in the centre of field while degrading towards corners; different designs result in very different performances in this range. Proposed values for F 2.8 – F4 are to be intended as top performance in the center of field. Due to lower MTF value of a real lens I pushed sharpening parameters a bit compared to the diffraction limited scenario, as halos on the low frequency edges are less probable to occur. Now let's simulate the same scenarios for a 36 Mpxls full frame Bayer Sensor:

Diffraction limited scenario:

1 2 MTF values for a MTF values for a diffraction limited lens + 36 Mpxls diffraction limited lens Full Frame Sensor Wavelenght of light = Wavelenght of light = 0.00055 0.00055 No Sharpening Sharpened MTF MTF MTF MTF MTF 50% MTF 10% F-stop 50% 10% 50% 10% Sharpening Parameters (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm)

2.8 247 532 4 173 373 5.6 123 266 66 105 91 105 K=0.35 r=1 8 86 186 58 102 89 105 K=0.5 r=1 11 63 135 49 88 72 105 K=0.5 r=1 16 43 93 37 71 61 97 K=0.6 r=1 22 31 68 29 56 49 86 K=0.7 r=1

Real lens scenario:

1 2 MTF values for excellent MTF values for for excellent real prime + 36 Mpxls real prime Full Frame Sensor Wavelenght of light = Wavelenght of light = 0.00055 0.00055 No Sharpening Sharpened MTF MTF MTF MTF MTF 50% MTF 10% F-stop 50% 10% 50% 10% Sharpening Parameters (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm)

2.8 247 532 41 88 80 105 K=0.5 r=1 4 173 373 41 88 80 105 K=0.5 r=1 5.6 65 195 47 95 80 105 K=0.5 r=1 8 53 159 41 88 80 105 K=0.5 r=1 11 45 135 37 82 77 105 K=0.65 r=1 16 38 91 33 70 67 105 K=0.7 r=1 22 28 68 26 56 60 100 K=0.8 r=1

At a first glance, with no sharpening applied, it seems that for a real lens at smaller apertures there is no performance gain in using a denser sensor: from F 16 on, both a Canon 5D MKII (diffraction limited at F16 according to previous assumptions) and a 36 Mpxls full frame sensor will perform at the same level with only marginal differences ( a few may occur from A/D converter and image processor performance). The same effect can be seen today comparing the MTF graphs from DXOmark at F 11 and F 16 for a Canon EOS 20D (same pitch than 5D MK II) and Canon EOS 500D (about same pitch of a 39 Mpxls full frame sensor). At F 11 the 500D still has an edge, at F 16 they have the same performance. But the real difference comes out when sharpening is applied: the denser pitch is able of recovering much more of the low MTF information coming from the lens , delivering details up to its higher Nyquist resolution limit. Moreover a denser pixel pitch will also allow higher sharpening parameters than a lower pitch, at similar Signal to Noise Ratio (that's the catch: hard to keep up the SNR while increasing pitch) In other words the effect of sharpening is boosted by the increase in sensor pitch. The difference will be more noticeable for big enlargements, digging into the low MTF zone. So more megapixels actually mean more information, but it becomes clear only after proper processing of the image.

Now let's get further and simulate the same scenarios for a 50 Mpxls full frame Bayer Sensor:

Diffraction limited scenario:

1 2 MTF values for a MTF values for a diffraction limited lens + 50 Mpxls diffraction limited lens Full Frame Sensor Wavelenght of light = Wavelenght of light = 0.00055 0.00055 No Sharpening Sharpened MTF MTF MTF MTF MTF 50% MTF 10% F-stop 50% 10% 50% 10% Sharpening Parameters (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm)

2.8 247 532 4 173 373 5.6 123 266 74 115 102 115 K=0.35 r=1 8 86 186 63 115 90 115 K=0.45 r=1 11 63 135 52 95 78 115 K=0.5 r=1 16 43 93 40 74 68 115 K=0.7 r=1 22 31 68 30 58 50 94 K=0.75 r=1

Real lens scenario:

1 2 MTF values for excellent MTF values for for excellent real prime + 50 Mpxls real prime Full Frame Sensor Wavelenght of light = Wavelenght of light = 0.00055 0.00055 No Sharpening Sharpened MTF MTF MTF MTF MTF 50% MTF 10% F-stop 50% 10% 50% 10% Sharpening Parameters (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm) (lp/mm)

2.8 247 532 44 96 90 115 K=0.65 r=1 4 173 373 44 96 90 115 K=0.65 r=1 5.6 65 195 50 105 90 115 K=0.55 r=1 8 53 159 44 96 90 115 K=0.65 r=1 11 45 135 39 89 88 115 K=0.7 r=1 16 38 91 34 74 74 115 K=0.75 r=1 22 28 68 26 58 69 115 K=0.85 r=1

All the evaluations made for the 36 Mpxls sensors are still applicable. After sharpening the 50 Mpxls sensor we get for every F-stop a + 10 lp/mm difference to the 36 Mpxls one and a + 20-25 lp/mm difference to the 21 Mpxls one. Sounds pretty good for a camera that is supposed to perform the same as the other two from F 8 down to F 22 due to diffraction. Probably however the smaller stops F 16 -F 22 will suffer from excessive sharpening at the proposed parameters and most user would settle with safer values. All the mayor sensor producers seem to actually own the technology to produce a 45-50 Mpxls full frame sensor; a full frame body with the canon EOS 7D pitch would be about 50 Mpxls. This is close to the Mpxls needed to sample a real excellent prime lens at F 5.6 - F 8. Given the performance of modern pro line primes, there is still enough information delivered to the sensor to make a big difference at F 5.6 , F 8 and maybe F 4. Furthermore, with such pixel density it would probably be possible to drop the antialias filter (Leica had done it with the M9!) an have a further boost in noise and sharpness (none in resolution), having the sensor resolve down to the Nyquist frequency with far less contrast loss, in a way similar to actual Foveon sensors (slightly less effectively). It could be possible to apply less sharpening.

With diffraction limited lenses the MTF at Nyquist would still be too high to allow dropping the antialias filter: artifacts would occur when shooting very fine and regular detail (think of the old Kodak DCS Pro 14n full frame camera). With a real lens however, the natural rolloff of resolving power gradually cuts out the higher frequencies that would induce aliasing near the Nyquist limit: the lens itself provides the necessary "antialias filter" for the sensor.

Noise performance and dynamic range with a 14bit A/D converter should still be good (think of Canon EOS 7D), just a small step (10-15%) behind Canon EOS 5D MKII. Sounds pretty usable to me. I probably would not need the extra file size for printing, but still it makes sense. I don't think actual sensor technology is worth pushing over 50 Mpxls, which I consider being the break even point considering pros and cons. Technology is already implemented but production costs would be much higher than Canon EOS 7D due to yield in sensor manufacturing. Given my typical use of camera, I'd be better served with a decent dynamic/noise range 32 Mpxls full frame sensor, still getting the most out of my old lenses; that would match the practical resolution of the top medium format film systems, while retaining the wider DOF of 35mm which helps a lot when doing landscapes. A 16-20 Mpxls full frame sensor, even with a 14 fps shooting rate, an extraordinary wide dynamic and noise range, simply do not appeal me much as I'm no sports or wildlife shooter.

3) File size and processing power

I don't see real problems here, at least outside the in-camera buffer. Actual 64 bit CPUs and Operative Systems allowed us to get rid of computing limitations experienced with big images on 32bit systems. I usually work with 300 Mb to 600 Mb files obtained scanning medium and slides; I frequently make panos in the 2-3 gb size range. A core i7 920 processor with 6 Gb ram is more than enough to handle this workflow; it's a pretty common and inexpensive configuration nowadays and computing times are acceptable in most of the cases. For large Gb images I simply crop a relevant smaller portion to make adjustments on and then save the workflow as a batch to be executed on the whole image; it's common practice for many photographers and allows to evaluate adjustments in real time even on large files.

A final consideration about APS-C and smaller formats. Given my max print size of A3 +, such a small sensor simply does not match my requirements: even with very high pixel densities (32 to 50 Mpxls) it would take a n almost perfect lens in the F 4 to F 5 range to deliver appropriate resolution to the sensor. There are many good APS-C lenses, but no one performing to that level. Noise would be hard to cope with and tonal separation would be considerably worse than full frame. Furthermore you lose the possibility to have a shallow DOF and shoot in available light conditions: there are a few nice full frame F 1 - F 1.4 lenses, but no equivalent F 0.6 - F 0.9 It's a no go for me.

The best upgrade pattern for an APS-C shooter not interested in printing extra- large would be moving to an equivalent full frame resolution sensor; a cheap (1000-15000 USD), fast 18 Mpxls full frame body would deliver a lot in terms of quality and usability and win the favour of many actual APS-C users. Make it a Foveon-like (multilayer) sensor, drop mirror/antialias filter and it's just the perfect recipe.

In my opinion, full frame DSLRs seem to have become what medium format once was (plus a much faster and easier workflow): the goldilocks of photography.

Final note on the biggest improvement I've seen in the market recently: the Sony/Fuji Electronic View Finders are an incredible feature that make the camera much more usable. An example to follow. Hope Canon finds its way to drop away that mirror...

The scenario I described gives me sort of an upgrade path for the future, with a very probable step up to a + 32 Mpxls and an eventual move to 50 Mpxls if and when they'll become accessible; I don't see a good point in moving on, unless a totally new, cheap technology is developed.

PART II – PRINTING PERFORMANCE

Foreword

Being the last step of the classic imaging chain, printing is a crucial process to which is due most of the impact that an image can deliver. Back in the analog era many famous photographers had built their reputation upon the special quality of their prints, which were able to capture the eye with better tones and sharpness than average prints could do. In the digital era inkjet printing changed the rules, raising the standard for sharpness and colour accuracy; however the printer is probably the weakest link in the whole chain, limiting the performance we can obtain from top modern equipment. Differences between modern DSLRs tend to be less relevant in the final print than in the original image to be printed, as viewed on a screen at high magnification; this is due to a degradation of performance at high spatial frequencies, depending on many factors, some of which mechanical (for ex. print nozzles and head carriage precision), some chemical (for ex. ink and paper quality), some purely information-related (for ex. dpi density and contrast in the input image). In other words printers will “flatten” the performance obtainable from the camera, both for low enlargements where performance is capped below the same level for different , and for very big enlargements where the original image may not contain enough information for an optimal feed to the physical print system. The scope of this document is defining where those limits lay for different full frame cameras and how much performance difference is to be expected on the same printer. The proposed method, as it involves some degree of judgement in assessing test data (mostly print MTF values), is not to be considered as an accurate description of absolute performance: other printers/paper combos could deliver different results; however I believe it offers a good estimate of delta in performance from different sensors on the same printer, which may be of interest for a user evaluating an upgrade of the camera but not of his printing gear.

General Printer Performance

A theoretical approach for evaluation of printer performance is hardly feasible: too many factors are involved and accurate modelization is beyond the scope for practical use; on the other side proper results are obtainable from empirical tests. I'll follow a "black box" INPUT-OUTPUT approach, borrowing concepts, method and some data from Norman Koren's site (http://www.normankoren.com/Tutorials/MTF3.html) and applying it to simulated scenarios, having verified in my experience that results match expected output quality. Test condition involves printing and evaluating a digitally generated simulation test pattern, upscaled to the required enlargement factor. For each one of the previously proposed full frame scenarios, the test pattern simulates performance with an excellent 35mm lens (think of a good sample of Canon 85mm F 1.8), for the plane of sharpest focus, with proper sharpening applied. Based on my empirical tests, for a good, user available photographic inkjet printer (tests were done with an Epson R1900 printer) we can assume the following top performance: - Top resolution (MTF 10%) of about 190-200 lp/in (line pairs per inch) on quality glossy photo paper; - MTF 50% (often associated with sharpness perception from “close inspection” i.e. about 10 inches distance) of about 155 lp/in (line pairs per inch) on quality glossy photo paper; - Printable dynamic range of about 6.6 stops on quality glossy photo paper (typical 100:1 contrast ratio or a Density of 2). Previous results are obtainable only with minimal software resizing ( up to 4x upscaling of original image to final print size), operated manually by user and not automatically by printer driver, very sharp original image, over 1000 dpi image density to printer, glossy photo paper; however performance also depends on orientation of details, with a maximum falloff of about 15-20 lp/in for the direction parallel to the print head (horizontal lines). Consequently for a real picture I consider the practical printer resolution limit to be about 175 lp/in; moreover it matches the resolution requirement for a 25 cm (about 10 inches) inspection by a 20/20 sighted individual. In other words if your final print will be made with an inkjet printer (as it is in most of the cases), it doesn't make sense, even in the best case scenario, to aim for higher than 175 lp/in print resolution or inspection closer than 10 inches for perfect 20/20 vision. In a real scenario previous results are hardly obtainable, as we'll generally feed the printer with less-than-optimal data; most photographers, consciously or not, usually accept much lower print quality.

The short story

An input density of 350 dpi is commonly considered enough for a sharp printer output, but in practice it involves accepting a maximum resolution of about 120 lp/in in final print for an optimal input image; that's 50 lp/in short of the best possible result from an inkjet printer, but still optimal for images taken with consumer-available camera equipment and enlarged to usual (8x10 inches plus) print sizes. For inkjet prints of very sharp images that must stand up to close inspection I suggest a higher setting, 450 dpi or better for a Bayer sensor generated image. (As a side note, tested but not included in this document, 350 dpi is enough for Foveon sensor generated images, due to higher pixel-level sharpness). Performance differences for cameras with full frame sensors are relevant from 4x enlargement and up, where 4000 dpi sensors (EOS 5D MKII) start to lose sharpness and resolution compared to maximum printable values; from 6x 32-36 Mpxls sensors will start to give ground and from about 9x also a 50 Mpxls sensor will. A very close (i.e. 10 inches) inspection distance is required to perceive those differences. Up to 16x enlargements delta in performance (both MTF 50% and MTF 10%) is more or less constant and equal to a +2 enlargement factor for each 1000 dpi increase in sensor density: a 21 Mpxls sensor at 8x enlargement will perform like a 32-36 Mpxls sensor at 10x and a 50 Mpxls sensor at 12x. Within this range however, a 50 Mpxls sensor will hold very fine details better (print MTF 10%), showing a very gradual falloff, while lower density ones will show a somehow steeper curve; this could make for a visible quality difference from close inspection distance. From 16x on, curves become more irregular (less than optimal information for the physical printing system) and differences start to be “flattened”; the denser sensor however will keep a significant edge over the others up to 20x or more (personal estimate, not tested: I don’t print that large).

The long story

Let’s consider a performance requirement roughly based on top obtainable resolution: following initial assumptions, to input the printer with a 175 lp/in @ 350 dpi we would need to sample with about 2 pixels for each line pair (1 line pair = 1 black line + 1 white line = 1 cycle), corresponding to 0.5 cycles per pixel, i.e. the Nyquist limit of the sensor, where MTF will ( and for a Bayer sensor should!) typically be below MTF 10%: that's an hardly usable contrast zone, where details and noise start to merge and image quality is very low. A decent scenario for a Bayer matrix sensor, with proper sharpening applied, could be 3 pixels per line pair ( 4 pixels would be even better). Thus to reach the 175 lp/in required for 20/20 vision you would need at best 1.5 times (3/2 ratio) that density, i.e. 525 dpi. Upsampling ( artificial increase in density) and then sharpening may provide a slightly better result, especially for big enlargements, but aliasing and artifacts become an issue and results really depend on the single image. I try to avoid resampling if I can. Print potential of a sensor is often evaluated without considering the degradation introduced by printers, i.e. shooting test targets and considering the top obtainable MTF50% value, expressed in a form that does not depend on physical size of the sensor itself. Often it is LW/PH (number of single white and black lines, i.e. line widths, per picture height, obtainable multiplying lp/mm by 2 and the by the sensor short size in millimetres); in this way you get an idea of “how many usable lines” you get from the sensor (regardless of its size) to be delivered to the printer or other visualization media. However the physical printing process will generally introduce a degradation in image quality, due to the previously listed mechanical, chemical and information-related factors; all those factors are convolved when it comes to final print quality and it's difficult to isolate their specific effect on performance. For example an input image could have proper density, i.e. over 500 dpi, while lacking the effective information (lp/mm) to deliver contrast needed for a sharp print; it could be the case for upsampled images or for areas of an image close to DoF limits. Borrowing the results from my previous document, in the following I'll propose an evaluation of performance in simulated scenarios for 21, 32-36, 50 Mpxls sensors. As a starting point I will discuss enlargement/print to the largest standard ISO 216 paper size still allowing a density to the printer of at least 350 dpi (unless differently noted); this is a typical setting used by many photographers for their quality prints. Then I'll draw some conclusions about performance differences for the more commonly used ISO 216 sizes (A4, A3, A3 +, A2). At first I’ll define a few parameters on which simulations are based:

The human eye: 20/20 Vision Criterion

The traditional definition of 20/20 vision for the human eye is based on a maximum resolution criterion, defined as an “angular perception ability”, i.e. the ability to distinguish patterns of alternating lines with a feature size as small as one minute of arc (1/60 degree or about 0,000291 radians). In other, less appropriate, words it’s the smallest angle by which the eye is still able to “tell a black line from a white one”, before perceiving both as a gray shade. Being an angular capability, the longer the distance, the bigger the size of minimum perceivable detail; that’s the reason why, from proper distance, even a not-so-sharp print could appear ok. However, similarly to camera lenses, a more extensive characterization of eye performance is possible using MTF curves, generally referred to as Contrast Sensitivity Functions (CSF); they are able to represent the response of the eye at different (angular) spatial frequencies, defining where the sensitivity is higher. The peak occurs generally between 6 and 8 cycles per degree. In the field of photography, perceptual methods have been developed over the years to modelize how this distribution of angular visual acuity is related to the contrast modulation (MTF curve) of an imaging system (lens+camera+sensor); the most widely used is the Subjective Quality Factor (SQF). For the scope of this document I’ll keep using the simpler, traditional 20/20 criterion as a reference for top resolution, relying on the MTF 50% parameter for sharpness assessment; it’s a reasonable, yet approximate, reference for a 10 inch distance inspection of prints, fitting the premise that we’re interested in evaluating top performance obtainable from printer, rather than optimal sharpness perception for different print sizes. Based on 20/20 vision criterion, the top resolution distinguishable by the eye from a distance of 250 mm (about 9.84 inches) is:

Min. dist. feature= distance x angle in radians = 250 mmx0.000291 = = 0.0728 mm

Converting to line pairs per millimetre, this value must be multiplied by 2 because the perceived feature corresponds to a line pair (black line+white line), so we get:

1/(0.0728x2) = 6.87 lp/mm or, in inches, about 174 lp/in

As previously stated, this value corresponds to the maximum practical resolution (MT 10%) obtainable printing a real image ( up to 190 lp/in for vertical lines if printing test targets, but I’ll stick to real use scenarios); thus 9.84 inches is the shortest viewing distance allowed by a top inkjet printer if you aim for a 20/20 vision criterion. Getting closer won’t improve perception of fine details.

As an important consequence, the admissible (CoC) for a 12.4 x enlargement (ISO 216 A3 from a full frame sensor) would be:

0.0728 mm / 12.4 = 0.00587 mm

Using this value with one of the many available DoF calculators, is easy to understand how becomes the main limiting factor for big enlargements with a 20/20 vision quality criterion: DoF becomes very shallow and to the F 11 – F 16 range is often mandatory; moreover to retain decent sharpness at DoF borders, proper sharpening is absolutely necessary. As we’ll see in the following, only a 50 Mpxls full frame Bayer sensor would provide (barely) enough performance to match this criterion for A3 enlargement, but only for ideal shooting conditions and with a perfect workflow.

The Camera: Simulated Specs

Following cameras have been simulated:

Camera Model Mpxls Sensor Pitch dpi (micron) EOS 5D MK II About 21 Mpxls 6.39 3975 EOS 5D MK III? About 32 Mpxls 5.16 4922 Nikon D800? About 36 Mpxls 4.9 5180 50 Mpxls EOS?? About 50 Mpxls 4.16 6106

- 21 Mpxls full frame sensor

21 Mpxls full frame sensor with excellent lense, proper sharpening, delivers in ideal conditions and for the plane of sharpest focus about 78 lp/mm @ MTF 10%, in the F 2.8 - F16 range. The 4000 dpi density allows for a 12.4 x enlargement factor (upscaling) to 11.69x16.54 inches (ISO A3 ) print size at 320 dpi ; in ideal conditions the camera would barely be missing the 6,8 lp/mm performance criterion, delivering 6.29 lp/mm ( 78 lp/mm / 12.4) at MTF 10%. However in practice, due to contrast losses in the upscaling process and physical printing of media, the top performance I can obtain in a print with this input parameters is 115 lp/in at MTF 10%, much lower than the maximum 175 lp/in obtainable in optimal conditions (A close inspection from a 10 inches viewing distance would reveal a difference, but it would become almost unrelevant from a distance of about 15 inches (exactly from 38 cm): given the standard viewing condition of such a large print, it's still an incredibly good result even for paranoid details peepers. Sharpness perception however, for a standard viewing distance of 10 inches is related to MTF 50% value; here the sensor native value strongly depends on values, but with proper sharpening we can assume 63 lp/mm in the range F 2.8 - F 11 It translates into about 90 lp/in @ MTF 50% in the final print: much lower than the maximum 155 lp/in obtainable in optimal conditions.

- 32-36 Mpxls full frame sensor

Considering the same print size to one of the standard ISO formats (A2, A3, A4 etc.), 36 Mpxls and 32 Mpxls sensors deliver very similar performance figures; following scenario is developed for a 36 Mpxls sensor but is applicable to a 32 Mpxls one with an acceptable margin of error (about - 5 lp/in @ MTF 50% and MTF 10%). 36 Mpxls full frame sensor with excellent lense, proper sharpening, delivers in ideal conditions and for the plane of sharpest focus about 105 lp/mm @ MTF 10%, for the F 2.8 - F16 range. The 5150 dpi density allows for a 13.8x enlargement factor (upscaling) to 12.95x19.01 inches (A3 plus) print size at 375 dpi ; in ideal conditions the camera would still be exceeding the 7 lp/mm performance criterion, delivering 7.6 lp/mm ( 105 lp/mm / 13.8) at MTF 10%. However in practice, due to contrast losses in the physical printing of media, the top performance I can obtain in a print with this input parameters is 120- 125 lp/in at MTF 10%, much lower than the maximum 175 lp/in obtainable in optimal conditions. A close inspection from a 10 inches viewing distance would reveal a difference, but it would become almost unrelevant from a distance of about 14 inches (exactly from 36 cm): given the standard viewing condition of such a large print, it's still an incredibly good result even for paranoid details peepers. Sharpness perception however, for a standard viewing distance of 10 inches is related to MTF 50%; here the sensor native value strongly depends on aperture values, but with proper sharpening we can assume 80 lp/mm in the range F 2.8 - F 8. It translates into about 95-100 lp/in @ MTF 50% in the final print: much lower than the maximum 155 lp/in obtainable in optimal conditions.

- 50 Mpxls full frame sensor

50 Mpxls full frame sensor with excellent lense, proper sharpening, delivers in ideal conditions and for the plane of sharpest focus about 115 lp/mm @ MTF 10%, for a usable F 2.8 - F22 range. The 6100 dpi density allows for a 17.5x enlargement factor (upscaling) to 16x23 inches (A2) print size at 350 dpi; in ideal conditions the camera would just barely miss the 20/20 vision performance criterion, delivering 6,57 lp/mm ( 115 lp/mm / 17.5) at MTF 10%. However in practice, due to contrast losses in the upscaling process and physical printing of the media, the top performance I can obtain in a print with this input parameters is 115 lp/in at MTF 10%, much lower than the maximum 175 lp/in obtainable in optimal conditions. A close inspection from a 10 inches viewing distance would reveal a difference, but it would become almost unrelevant from a distance of about 15 inches (exactly from 38 cm): given the standard viewing condition of such a large print, it's still an incredibly good result even for paranoid details peepers. Sharpness perception however, for a standard viewing distance of 10 inches, is related to MTF 50%; here the sensor native value strongly depends on aperture values, but with proper sharpening we can assume 90 lp/mm in the range F 2.8 - F 11. It translates into about 90 lp/in @ MTF 50% in the final print: much lower than the maximum 155 lp/in obtainable in optimal conditions.

In the following I’ll propose a table with test results for different enlargement factors up to A2 print size; a graph is also included, with trend lines interpolating empirical data. I believe it could be useful to evaluate by a quick glance the expected print performance for the three sensors. Lines of the same colour are referred to the same sensor. For different enlargement factors, dash lines represent ultimate practical resolution (MTF 10%) i.e. the finest perceivable details; solid lines are indicative of sharpness perception from a close distance (about 10 inches). It’s important to note that sharpness perception from longer distances is not directly relatable to the MTF data shown in the graph, as visual acuity of human eye seems to have a rather complex behaviour. Perceptual models have been developed to match it, the most widely used being the Subjective Quality Factor (SQF), implementing a few different modelization criteria. Discussing SQF is beyond the scope of this document, however it may be interesting to know that in its classic formulation it states that sharpness perception for human eye is related to the area of MTF graph enclosed between 3 and 12 cycles per degree or between 0.5 and 2 x image magnification when MTF is expressed in logarithmic scale, as in my previous document. The previous result, although being obtained from the analog print process and not directly applicable to digital printing, is useful to draw a few general guidelines about sharpness perception. Perceived sharpness for a 35mm enlarged 12x would be related to the area enclosed by 6 -24 lp/mm; for a 8x enlargement would be 4-16 lp/mm; for 20x would be 10-40 lp/mm. So we could get to the paradox that a same image, taken with a lense designed for ultimate resolution over contrast, could appear not so sharp for low and modest enlargements and quite sharp for bigger enlargements, where the high spatial frequencies are involved in sharpness perception. An analogy for digital could be that sharpening with wider a radius is generally more appropriate when aiming to smaller prints/higher dpi settings, while lower radius pays off better for larger prints/lower dpi settings; of course contrast in the original image is relevant in choosing the proper parameters. In other words consider that sharpness perception at different viewing distances should not be induced on the basis of the proposed graph; it may be useful however as a general indication of how much performance we can “squeeze” out of the printer, with different sensors and optimal workflow.

EMPIRICAL TEST RESULTS – SIMULATED SCENARIOS

ENLARGEMENT FACTOR

A4 A3 A3 + A2 1.00 4.00 6.00 8.00 8.70 10.00 12.00 12.40 13.80 14.00 16.00 17.50

EOS 5D MKII

Print lp/in MTF 175.00 175.00 175.00 165.00 155.00 140.00 120.00 115.00 112.00 110.00 105.00 80.00 10% Print lp/in MTF 155.00 155.00 140.00 130.00 125.00 115.00 95.00 90.00 90.00 87.00 80.00 65.00 50% Print dpi (approx.) 4.000 1.000 670 500 450 400 330 320 290 285 250 225

32 -36 Mpxls EOS?

Print lp/in MTF 175.00 175.00 175.00 175.00 175.00 165.00 147.00 140.00 125.00 123.00 117.00 105.00 10% Print lp/in MTF 155.00 155.00 155.00 145.00 143.00 130.00 115.00 110.00 100.00 97.00 90.00 80.00 50% Print dpi (approx.) 5.200 1.300 870 650 600 520 430 395 375 370 325 300

50 Mpxls EOS?

Print lp/in MTF 175.00 175.00 175.00 175.00 175.00 175.00 170.00 165.00 150.00 145.00 125.00 115.00 10% Print lp/in MTF 155.00 155.00 155.00 155.00 155.00 150.00 130.00 125.00 115.00 112.00 97.00 90.00 50% Print dpi (approx.) 6.000 1.500 1.000 770 700 600 510 490 440 435 380 350

Required Distance for Print Contrast 20/20 Vision Inspection (Tested with Epson R1900 inkjet on Epson Premium Glossy Paper) Criterion 180.00 9.8 inches 170.00

160.00 10.5 inches

150.00

140.00 12 inches

130.00

120.00

14 inches

110.00

Print Print 100.00 17 inches

90.00 Line PairsInch Line per 80.00 21.5 inches 70.00

60.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 A4 = 8.7 x A3 = 12.4 x A3+ = 13.8 x A2 = 17.5 x

Enlargement Factor / Print Size 50 Mpxls EOS? Print lp/in MTF 10% 50 Mpxls EOS? Print lp/in 50% 32-36 Mpxls EOS? Print lp/in MTF 10% 32-36 Mpxls EOS? Print lp/in MTF 50% EOS 5D MKII Print lp/in MTF 10% EOS 5D MKII Print lp/in MTF 50% The simulated performance is obtainable only for the plane of sharpest focus. However it must be considered that for big enlargement factors, only a small portion of the image will be really sharp and in-focus, while contrast, both in the original image and in the print, will degrade towards DoF borders. This effect can be functional to image quality if selective focus is required (i.e. portraits, isolation of subject from background etc.) but generally becomes an obstacle for landscape shooters seeking hyperfocal distances. Using software DoF calculators, the proposed performance scenarios can offer some practical guidance about optimal CoC setting for different enlargement factors. In other words, we need to be aware if and when printer is limiting our optimal Circle of Confusion setting; if the whole camera + printer chain is not able of delivering, in the best case scenario i.e. FOR THE PLANE OF SHARPEST FOCUS , the necessary MTF value for the 20/20 vision criterion at selected view distance, then we may say that the system is “print limited”. In this condition it doesn’t really make sense to aim for a 20/20 DOF criterion when taking a picture, and relaxing the requirements may help to obtain better print performance. From previous graphs we can see that EOS 5D MKII is not print-limited up to 6x, then performance starts to drop below top level. A 32-36 Mpxls full frame sensor is not print-limited up to 8.7x (ISO A4). A 50 Mpxls full frame sensor is not print limited up to about 12x (close to ISO A3). It means that up to those respective print sizes you’ll be able to appreciate fine details from a close 10 inches view distance, within a usable F-stop range of F2.8-F11 (still delivering top sensor performance after proper sharpening); stopping further down will subtract sharpness, probably bringing performance below optimal level. F16 with sharpening is probably still usable even for a 50 Mpxls sensor: even if the system is diffraction limited, the effect of sharpening is boosted for denser sensors, allowing for a better recovery of high-frequency detail. In a practical scenario, knowing that a 21 Mpxls sensors (EOS 5D MKII) will provide, in optimal conditions., only less than 120 lp/in at ISO A3 print size, it makes no sense setting a 20/20 vision - 10 inches view distance criterion for DoF calculators. However setting CoC requirement at best to 0.00858 mm , corresponding to about 120 lp/in at a distance of 10 inches, then focusing to the calculator indicated would allow for a wider DoF and best possible printer performance for that enlargement size. For practical purposes I propose the following table indicating optimal CoC settings for the three full frame sensors and for enlargements to different ISO 216 print size.

A4 A3 A3 plus A2 INKJET PRINT TO ISO 216 SIZE: 8.70 x 12.40 x 13.80 x 17.50 x 50 Mpxls EOS? - Print Limited Performance 175 lp/in 165 lp/in 150 lp/in 115 lp/in Optimal CoC setting for DoF Calculators (mm) 0.00836 0.00621 0.00613 0.00631 32-36 Mpxls EOS? - Print Limited Performance 175 lp/in 140 lp/in 125 lp/in 105 lp/in Optimal CoC setting for DoF Calculators (mm) 0.00836 0.00732 0.00736 0.00691 21 Mpxls - EOS 5D MKII - Print Limited Performance 155 lp/in 115 lp/in 110 lp/in 80 lp/in Optimal CoC setting for DoF Calculators (mm) 0.00941 0.00891 0.00836 0.00907 From the previous table we can see that sometimes decrease in printer performance (print limited performance) will limit the perceivable details, compensating for the shallower DoF requirement from big enlargement: as a result, optimal CoC setting will stay more or less constant up to big enlargement factors. We can also see that a 50 Mpxls sensor can perform at size A2 like a 21 Mpxls one at size A3 (about 115 lp/in), but CoC setting and thus DoF requirements become more stringent, forcing to stop down beyond optimal values and then pushing sharpening to regain contrast. Proposed CoC settings, although being close in absolute values, can make a difference in the field, allowing to gain 2 to 4 meters in near DoF limit when shooting at hyperfocal distance: enough to be relevant to the “accurate” landscape shooter.

Conclusion

Judging print quality by measuring data on original image only (even with perception- oriented methods like SQF) could be deceiving because the printer will introduce its own attenuation of the image, progressively dampening response at higher frequencies especially for big enlargement where decreasing image density will compromise contrast available in the original image. The proposed test results, although being obtained from a specific inkjet printer, could offer a general guideline for evaluation of imaging chain performance and how much improvement is to be expected from future full frame bodies. I consider a 32-36 Mpxls full frame sensor to be the best trade-off between low light shooting capability and printing performance, being able to produce, in conjunction with a good inkjet printer, an image of size A3 + and 120 lp/in, matching maximum eye resolving power from 14 inches view distance while still appearing sharp at close inspection distance. A 50 Mpxls sensor could still make sense, provided that frame-rate and high-ISO issues could be addressed by future technological developments.