[Douglas_of_Sweden]

I have a technical application at work. We do research on how waves that break at sea form white caps, and how the bubbles in the white caps burst and eject tiny droplets into the atmosphere which we call sea spray. These droplets aka aerosol particles have for example climate implications. Try holding a hand over a glass with mineral water and you will feel similar droplets hit your skin.

What I want to do now is to photograph the bubbles at the surface of the water in a laboratory environment. We know from before that the bulk of these bubbles are 0.1 to 0.2 mm in diameter, and that the number of bubbles then gradually decrease with increasing size up to a small number of bubbles of several mm (assuming that we talk about sea water with a salinity around 3.5%, in fresh water you get much larger bubbles, and less of them). At the lower size range previous experiments mostly go down to about 30-50 micrometer (0.03-0.05 mm) because the digital video records used to count these could not resolve smaller bubbles. But some recent studies suggest the existence of even smaller bubbles. We actually don't know the lower limit in size. Now those studies used very expensive high speed high resolving cameras. I don't have room for that in my budget right now, and no use for the high speed. But I do have a couple of DSLRs, and several decent 1:1 macro lenses. And I've been thinking that I should be able to do better with modern APS-C sized sensor than they did a couple of years ago with tiny video camera sensors.

Assuming that I mount the camera looking downward some 10-50cm above the water surface with a 1:1 macro at its close focus range, have a good lightening etc and start making bubbles. What could I resolve? We will test it of course, but from a more theoretical point, could one predict how small things we could resolve?
I presume that the pixel size of the sensor matters?
And the lens resolution?
What else?
How do I estimate the size of the smallest subject I could resolve?

Many thanks in advance for any help with this.

[enoeske]

I don't know the theoretical limit (I suppose anything smaller than 1 micro px site in the sensor) but you can capture some pretty small things with macro gear.

tiny water drops on a leaf


sweat glands in a finger tip


furry bee covered in pollen


bugs micro lens eyes

[stanislav]

Well you are talking here about 2 different resolutions:

1. The smallest thing that can be resolved is in the magnitude order of the light that is being used. So for visible light it is in range of 400-700nm. That limit has nothing to do with the resolution of sensor, but due to physics. That is wy electronic microskopes are used when higher resolution is required.

2. Macro 1:1 means that the image on sensor is eqaually big as the object in reality. Assuming that you have focus on 1:1, that the bubbles are in focus and that you are using K5 you get following result: sensor size is 23.7mm X 15.7mm and the resolution is 4928x3264. With some calculation it ends that a single pixels size is about 4.8um X 4.8um (micrometers). So in theory you have horizontal and vertical resolution of about 5um and diagonal resoultion of about 6.8um. Now every of those pixels capture only one colour (red green or blue) so there is some interpolation taking place where neighbour pixels are used to decide the colour of each pixel. With that in mind, I would say that the best you can achieve (with 1:1 macro) is about 10um.

Now to some practical aspects:
You have to have a fairly long focal range on your macro lens so that it does not get stained when you take photos (90mm or more - so that you can have some distance towards the subject). In 1:1 macro the DOF is paper-thin (at 2.8 or 3.5) so you need to step down the apperture significantly (so that you gain some DOF) to say at least f11 or more. Then you need some light as well (flashes or some lamps) and you'll have to experiment so that you get enough lite for your experiment.

Another consideration is that you ideally want significant DOF, low ISO (to minimize noise) and short shutter time (those bubbles are fast I guess). So to make it feasible you need huge amount of light, and I mean HUGE. It is doable, but I guess it won't be easy task

[Catalana]

So to make it feasible you need huge amount of light, and I mean HUGE. It is doable, but I guess it won't be easy task

A carbon arc lamp should do the trick, :-)

[newarts]

This is may be an ideal case for really cool work, especially if you can set up for "dark field illumination". In this case the field is brightly illuminated from the side so that if there's nothing in the field of view, it is dark - however, if a small bubble enters the field it will act as a point source of light - that's how we see bubbles in the first place. It is easy to see the effect by placing a jet black background behind a glass of soda water - side lighting of the bubbles creates bright, beautiful points of light.

In dark field work there is no limit to how small a bubble or droplet can be detected - so long as it scatters light you'll know it is present, but there are some limits to getting an accurate image of it. If a bubbles image is smaller than an individual sensor pixel we are at a limit: that is, if only one pixel lights up, all we can say is there is a bubble equal to or smaller than that size.

Two things to consider are the lens & its optics and the sensor; both have potential limitations.

Sensor
The K-x sensor has some 4288 pixels in the sensor's 23.6mm horizontal direction for a pixel diameter of about 5.5 micrometer, so that effectively sets the lower limit on the size of a spot of light that can be detected. However, the camera also has an AA filter that smears that out a bit so the pixel size is a fuzzy limit at best.

Lens
Diffraction spreads a point of light into a disk. The equation relating the disk size (Airy Disk) in this situation is:

Diameter = 2.44N(1+m/p)Wavelength

where N is nominal f-stop (what the f-ring says), m is magnification, and p is pupillary ratio (diameter ratio of apparent exit :entrance apertures

N(1+m/p) is called the effective f-number & can be found experimentally; set your lens at zero mag & point it at a uniform light source. Note the exposure time, then extend the zoom to the magnification you need & note the new exposure time; The ratio of the exposure times is the (1+m/p) factor.

The wavelength for blue light is about 0.4micrometers, so the disk diameter in blue light is (assuming p=1):

diameter(micrometers) = 2.44N(1+m/p)(0.4) ~ 2N(1+m)

If we set the airy disk diameter equal to that of the sensor pixel, it will indicate the optimum f-number to use; for the K-x at 1:1,

N=5.5/(2(1+1) ~ 1.2!!!

This would be right for a perfect lens, but our lenses are not that good! Presuming that optimum sharpness is around f:5.6, the Airy Disk diameter will be

Diameter = 2(5.6)(1+1) ~ 22.4 or about 4 K-x pixels

This should enable the imaging of the two opposite walls of a 20 micrometer bubble.

Set your flash to shoot sideways, parallel to the field in focus. Increase the flash speed if needed to stop motion.

Good luck, it sounds like fun.

[sergysergy]

sweat glands in a finger tip

amazing

[stanislav]

Some coffee bubles



A 1:1 macro of a lower (it seems that individual pollen particles cane be seen)



And a crop showing the individual pollen:

[monochrome]

Sounds like a question for falconeye

[newarts]

I hope the math didn't bury the conclusions in my earlier post: https://www.pentaxforums.com/forums/photographic-technique/174848-what-smalle...ml#post1818925

The smallest bubble that you can detect will be limited by:
Sensor Pixel size - any bubble smaller than a sensor pixel still will illuminate a whole display pixel - so the sensor pixel size is one limit.
Lens Diffraction effects - increasing f-stop & magnification increases the spot size at the sensor -a spot should be smaller than the sensor's pixel size if possible - but that's probably not possible for high resolution sensors

It looks like diffraction effects will limit the lowest resolvable bubble diameter to a few (maybe 3-4) sensor pixels with a 14mp sensor: at a 100% crop a 20micrometer bubble or drop will be seen as a fuzzy disk maybe 3/4mm diameter.

I hope I made an error because this less resolution than I thought it'd be.

[falconeye]

Sounds like a question for falconeye

ok, I'll bite

Assuming that I mount the camera looking downward some 10-50cm above the water surface with a 1:1 macro at its close focus range, have a good lightening etc and start making bubbles. What could I resolve?

newarts got the math out, so no reason to reiterate here.

IMHO, most important lesson from newarts comment: you need large F-stop for DoF and small F-stop for less diffraction. If everything is done in an optimal way (microscope), you resolve objects the size of the wavelength (0.5 µm) and below using coherent light sources and some smart software.

However, large F-stop and small F-stop are in conflict. So, a more interesting question is what is achievable in practical terms.

The attachment shows an image I took from a bee, showing one of its compound eyes. A worker bee's compound eye consists of 9000 ommatidia, each about 20 µm ( http://www.trin.cam.ac.uk/horacebarlow/8.pdf ) in diameter. The first attachment is the image I took with a K20D, the second is an 100% crop from the region showing the reflection in the eye.

An ommatidia is about 50 pixels large which in the photograph (if the size is 20µm) would translate to 0.4µm per pixel. However, I know the actual magnification (6x) and pixel pitch (5µm), so a pixel is actually 0.83µm large, i.e., an ommatidia in my image is 40µm large. This much for the credibility of scientific sources about bees ... Anyway, there is no way to see a bee's ommatidia with your naked eye.

However, the smallest detail is well below an ommatidia. It is about 3 pixels which is one line in the interference line pairs (2.5 µm). I would say the smallest structures resolved are about 2µm or a bit less. The interference is created by the light interfering with the reflection from the ommatidia's bottom end.

At the same time, you see the infinitesimal DoF.


So, for your sea spray experiment, you have exactly one way to go (if hunting for best results):


1. Set up a beyond 1:1 macro assembly. A 1:1 macro limits you to about 7µm. This is how I did it:
- Mount a DA*300 to the body, wide open
- Use a reverse filter ring and screw to the DA*300
- Screw a Zeiss 50/1.4 to the other side of the filter ring.
- Focus both lenses to infinity, set the Zeiss to F/4.
Considerations:
- Magnification is 300/50 or 6x.
- Resolution is limited by the Zeiss center resolution at infinity focus only. Which is best at F4. The diffraction limit at F4 is 0.55µm*1.22*4/2 = 1.3µm but at F4, you have a mix of 50% diffraction limit and 50% classical lens blur. So, practical resolutions for medium contrast subjects of 2µm are as good as it gets. Don't use a larger or smaller aperture or lesser lens. The resolution will suffer.

2. Use a flash at half or quarter power. Motion blur at these sizes will be huge and you need the light! 2µm at 5km/h translate to 1/360,000s! Flashes at full power are not fast enough.

3. I think, You really *must* mount the camera horizontally above the water, looking parallel to the water surface. Protect from the spray but there is no alternative. You can mount at different altitudes to measure how density reduces with height. Use a black surface as background. Flash from the side, making the spray stand out against the black background.

4. You will only see a "slice" of droplets due to the limited DoF (at a distance of 46mm from the open lens mount). But you'll see deeper if droplets are larger. So when counting them, you'll have to correct for this effect, e.g., by imposing a minimum edge sharpness of vertical edges in order to count them. Edge sharpness can be measured programatically.

5. There is no need for video. Video would reduce the available resolution a lot and results would be too blurry anyway to be useful.

6. Speed of droplets can be determined theoretically (how their density decreases with height) or from the difference of horizontal and vertical edge blur (motion blur).

[monochrome]

Wow! Thanks for the response!!

[Docrwm]

ok, I'll bite


newarts got the math out, so no reason to reiterate here.

IMHO, most important lesson from newarts comment: you need large F-stop for DoF and small F-stop for less diffraction. If everything is done in an optimal way (microscope), you resolve objects the size of the wavelength (0.5 µm) and below using coherent light sources and some smart software.

However, large F-stop and small F-stop are in conflict. So, a more interesting question is what is achievable in practical terms.

The attachment shows an image I took from a bee, showing one of its compound eyes. A worker bee's compound eye consists of 9000 ommatidia, each about 20 µm ( http://www.trin.cam.ac.uk/horacebarlow/8.pdf ) in diameter. The first attachment is the image I took with a K20D, the second is an 100% crop from the region showing the reflection in the eye.

An ommatidia is about 50 pixels large which in the photograph (if the size is 20µm) would translate to 0.4µm per pixel. However, I know the actual magnification (6x) and pixel pitch (5µm), so a pixel is actually 0.83µm large, i.e., an ommatidia in my image is 40µm large. This much for the credibility of scientific sources about bees ... Anyway, there is no way to see a bee's ommatidia with your naked eye.

However, the smallest detail is well below an ommatidia. It is about 3 pixels which is one line in the interference line pairs (2.5 µm). I would say the smallest structures resolved are about 2µm or a bit less. The interference is created by the light interfering with the reflection from the ommatidia's bottom end.

At the same time, you see the infinitesimal DoF.


So, for your sea spray experiment, you have exactly one way to go (if hunting for best results):


1. Set up a beyond 1:1 macro assembly. A 1:1 macro limits you to about 7µm. This is how I did it:
- Mount a DA*300 to the body, wide open
- Use a reverse filter ring and screw to the DA*300
- Screw a Zeiss 50/1.4 to the other side of the filter ring.
- Focus both lenses to infinity, set the Zeiss to F/4.
Considerations:
- Magnification is 300/50 or 6x.
- Resolution is limited by the Zeiss center resolution at infinity focus only. Which is best at F4. The diffraction limit at F4 is 0.55µm*1.22*4/2 = 1.3µm but at F4, you have a mix of 50% diffraction limit and 50% classical lens blur. So, practical resolutions for medium contrast subjects of 2µm are as good as it gets. Don't use a larger or smaller aperture or lesser lens. The resolution will suffer.

2. Use a flash at half or quarter power. Motion blur at these sizes will be huge and you need the light! 2µm at 5km/h translate to 1/360,000s! Flashes at full power are not fast enough.

3. I think, You really *must* mount the camera horizontally above the water, looking parallel to the water surface. Protect from the spray but there is no alternative. You can mount at different altitudes to measure how density reduces with height. Use a black surface as background. Flash from the side, making the spray stand out against the black background.

4. You will only see a "slice" of droplets due to the limited DoF (at a distance of 46mm from the open lens mount). But you'll see deeper if droplets are larger. So when counting them, you'll have to correct for this effect, e.g., by imposing a minimum edge sharpness of vertical edges in order to count them. Edge sharpness can be measured programatically.

5. There is no need for video. Video would reduce the available resolution a lot and results would be too blurry anyway to be useful.

6. Speed of droplets can be determined theoretically (how their density decreases with height) or from the difference of horizontal and vertical edge blur (motion blur).

+1 to you for that - technical but comprehensible (the best kind of answer). Thanks.

[Docrwm]

I don't know the theoretical limit (I suppose anything smaller than 1 micro px site in the sensor) but you can capture some pretty small things with macro gear.

tiny water drops on a leaf


sweat glands in a finger tip


furry bee covered in pollen


bugs micro lens eyes

The EXIF data isn't associated with your images, I'd love to know the setup and settings for your pics because they're terrific

[johnmflores]

I've photographed small children and toddlers with dSLRs. I've even photographed newborns...

...oh wait...nevermind...

[Rusty Rat]

Just one more example of resolving power, this time of machining marks on a fly fishing reel. The hotspot near the "WA" of Watergrip contains machining marks that are not visible even at 100% magnification. 200% shows marks that look little zigzag designs. This shot was taken using a 10mp K10 and a 35mm f2.8 DA macro.