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Elements of optics and basic physics
Understanding underwater photography
Elements from a course session on underwater optics offered by Cinemarine
Jacques Chenard - Christian Petron.
2011 Digital Edition
1 General......................................................................................1
2 The water environment.............................................................1
3 Reminder of some land photography definitions......................4
4 Basic reminder of elements of a camera...................................7
5 Reminder of Optical elements in photography........................8
6 Application of optical laws to the underwater medium..........11
7 Characteristics of natural light................................................16
8 Image contrast.........................................................................18
9 Variation of size of an apparent focal image..........................21
10 Geometric distortion associated with a flat port....................23
11 Chromatic aberrations linked to refraction in water.............26
12 Spherical aberration..............................................................27
13 The principle of aberration correction.................................29
14 Correction systems................................................................30
1 General
Different Technique
Underwater photography is a distinctly different technique to land photography, even if it is
usually carried out using the same equipment, however modified. Of course, working in water, an
environment with physical characteristics that are different to those of air, using equipment
designed to operate in air can only yield satisfactory results if the land photographer makes a
number of corrections to his usual habits. It is obviously possible to make these corrections by the
“trial and error“ method, otherwise known as considerable practice. Such an approach hardly
satisfies the spirit and is already extremely costly for land photography, and is frankly prohibitive
for underwater photography considering the means required. Of course you can always have a
try with so-called disposable cameras, but here we are talking about amusement, not underwater
photography. So it is a good idea to consider the extent to which the rules we usually follow, even
unconsciously, in land photography will need changes both in our thinking and in our actions as
we find them impossible to follow in the underwater environment. We intend to explain these
rules on the following pages, to review them briefly and to show their application to the specific
situations that interest us. This will sometimes require the help of a little mathematics, but we
need not go to incomprehensible limits for this. The formulae are shown more to allow the
operator to calculate the likely results rather than as a demonstration incomprehensible limits for
this. The formulae are shown more to allow the operator to calculate the likely results rather than
as a demonstration.
2 The water environment
Underwater photography
Underwater photography takes place, by definition, in the water, with both the operator and
the subject immersed. There can be exceptions to this, such as photos taken through a glassbottomed bucket or through the windows of an aquarium – situations that do not change the
optical problems encountered at all, even if they result in far greater comfort for the operator.
Water is a liquid medium, with a density of 1, that is about 800 times the density of air,
slightly viscous, a poor conductor of heat and of electricity and a universal solvent. This is true of
water defined as pure, even distilled.
We differentiate between fresh water, as found in lakes and rivers, which contains little
metallic salts in solution, and sea water, which contains up to 25 0/00 of sea water an excellent
electrolyte, hence its corrosive effect which attacks all types of metal, at varying speeds, by the
phenomenon of electrolytic transfer. This must be taken into account when designing housings
for still and cine cameras. When components in different metals or alloys are used, the
combination of metals should be selected which is not likely to form an electric cell, to avoid the
possibility of them welding to each other.
Anodes of zinc, or preferably magnesium, as fitted to ships’ hulls, are also strongly
recommended for professional metal housings which are always in the water. These anodes
attract the electrolytic current and are attacked before the metal parts of the housing. The
question does not arise in the case of plastic housings as plastics resist seawater well.
Pressure:
Water density has two main consequences: the first is due to the application of Archimedes
Principle: the apparent weight of an apparatus immersed in water is equal to the weight of the
apparatus in air less the weight of the volume of water that it displaces. For example, a housing
with a volume of 6 litters weighs 6.5kg complete with its camera, but when in water weighs
only 500g. This effect is one of the few positive points of underwater photography.
The second is that any object immersed in water is subject to a force on each part of its
surface equal to the weight of the column of water above it. The force increases with increasing
depth. This force is expressed in units of bars.
(1 bar = approximately 1 kg/cm2). Since the density of water is about 1, the pressure on
each square centimeter of the object’s surface corresponds to the weight of a column of water
with a section of 1 cm2, giving 1bar for every 10 meters.
To illustrate this problem, let’s say we have a porthole 12cm in diameter. At a depth of 50
meters the force bearing on the outside of this porthole is 678 kg/force; so under such
conditions the housing will need to be built with extremely strong materials, and special attention
will need to be given to making it watertight.
These problems are considerably complicated in housings or hulls that are intended for use at
extreme depths such as submarines or ROVs.
Under these extreme conditions the housings can be subjected to a pressure of several
hundred kilos per square centimeter resulting in portholes of very complex design made from
distorting material fitted to conical seatings. These portholes are designed to fit correctly and to
offer their optimum optical performance only at certain depths.
But let us get back to the standard housing where we already have a number of Corrosion:
Corrosion:
The corrosion problems are mentioned above, electrolytic deposits which develop around the
seals (usually in the form of insoluble metal chlorate deposits). This is why housings must be
carefully rinsed and brushed after each season to eliminate any white deposits, sometimes
confused with sea salt deposits.
The electrical conductivity of seawater is also a major source of problems in that we are
obliged to use watertight connectors for all cables connecting the housing with the flashguns. The
use of slave techniques to fire series of flashes is a major advance, avoiding the need for cables for
connecting synchronized light sources.
Electrical leaks coming from faulty watertight connectors to video and cine lights
considerably increases the problems of electrolysis on housings constructed of different materials:
Water has conductivity and whether it is significant or even less than that of metals, the electrons
still seem to find their way into places you would rather they did not go, particularly on
assemblies using different metals where they increase the natural “battery” effect.
Other corrosion phenomena:
The solubility of water is not limited to solid elements but also includes gases, notably
atmospheric gases (oxygen, nitrogen, etc.). We can define a saturation state of a given element in
water, corresponding to the maximum quantity of the element that can be dissolved in given
conditions. Water has a solubility tension that will tend to balance the pressure of the element in
the liquid. In very simple terms, the element not yet dissolved will try to enter the solution but is
rejected by the element already dissolved. The level of the saturation state is influenced by several
factors, principally the temperature and, for a gas, the pressure. If the liquid has reached a given
saturation state at a given pressure, it will be possible to increase the amount of dissolved gas by
increasing the pressure on the liquid. If the pressure is decreased the gas will tend to be released
spontaneously. In the same way, solid elements will tend to crystalize spontaneously if the
temperature drops below the level of complete saturation. These phenomena are well known to
divers since they are the cause of decompression incidents; we will meet them again later when
they unexpectedly occur in the optical field
3 Reminder of some land
photography definitions
Light travels in straight lines, at a speed that depends on the medium through which it passes.
In a vacuum, the speed is about 300 000 km/s. At the interface between two media, water and
air, its path is deflected, which we call refraction.
This fact is easily illustrated by a stick placed in water: the stick appears broken where it
enters the water. It is quite possible to calculate the deflection of the surface, but above all by the
a feature of every medium traversed: its refractive index.
This index is defined as 1 for air, 1.33 for water (average) and 1.5 for glass. The knowledge of
the refractive phenomena is fundamental in optics as this law governs the way in which a lens
works and, of particular concern to us, the path of the light rays coming from the subject to the
film or the video cells A fundamental rule in photography:
Descartes Law:
If a light ray passes from a medium with a refractive index of n1 to a medium with a
refractive index of n2 making an angle in medium n1 from the perpendicular at the interface
separating the two media, the angle r which it will make.
Basic principle of refraction and angle limit
Total Reflection
(Legendes):
Partly reflected ray / Rayon partiellement réfléchi
Incident ray / Rayon incident
Air (index=1) / Air (index=1)
Water (index=1.33) / Eau (index=1.33)
Refracted ray / Rayon réfracté
Angle limit R /Angle limit R
Incident ray / Rayon incident
Reflected ray / Rayon réfléchi
Other corrosion phenomena:
We will see that if medium n2 is more refractive (has a higher refractive index) than medium
n1, the ray will have the tendency to approach the perpendicular, and to move away in the
opposite case. In the situation that we are generally interested in: the passage from the water
medium to the air medium we note that a cone of light tends to open on passing through the
interface (or dioptre) water air.
There is a specific case: where the value of the sine is 1, and corresponds with an angle of
90°, as when the ray passing into air goes parallel to the surface interface. This gives n1 for the
air medium and n2 for the water medium, i is the angle in air and r the angle in water, we have,
Since i = 90°
n1 = n2 sin r
so, since:
n1 = 1 et n2 = 1.33
r = arc sin n1 / n2 1 = arc sin 0,75 = 480 45’
Thus if the incident angle in water has this value, the refracted angle in air will be 90° and
the ray will be parallel to the surface interface. If the incident angle has a value higher than
48°45’, the ray will simply be reflected by the interface, as if by a mirror. We will understand that
under such conditions it would be inadvisable to use a flat port with a wide-angle lens. On the
other hand, we note an important point: any ray passing perpendicularly to the surface is not
refracted.
Pane with parallel faces:
Apparent distance in water
If an observer examines a point P through a pane with a medium index of n and a thickness
e, he will see in reality an apparent point P’, whose position relative to P
is given by the equation:
PP’ = e(1 – 1 /n)
Point P’ will be closer to the observer if n > 1 (1 being the index of air where the observer is
situated), further away if n < 1.
In the case of a diver, whose eyes are in air, or a camera which is in the same position, we can
consider that the immersed object is separated from the observer by two distinct parallel faces:
the glass of the mask or the housing port, with a negligible thickness, and the thickness of the
water making up the main distance to the subject. If we apply the above equation, with n= 1.33,
and d the real distance between the observer and the subject, we have an apparent d’, where d’
= 0 75 d
Any object will therefore appear, to the diver as well as to his camera, as long as his
housing has a flat port, nearer than it really is, the real distance being 1.33 times the apparent
distance..
4 Basic reminder of elements of
a camera
Feature of a lens:
We limit ourselves here to a few definitions that will help us understand what is to
follow.
Focal length of a lens
Is a fundamental specification of this element, which depends only on the curve of the lens
and the refractive index of the glass used. In the case of a lens made up of several elements, the
focal length is the result of the focal length of the lens elements and the distances which separate
them. It is also the distance between the optical centre of the lens and the film plane, when the
camera is focused on infinity. The angle of view of the lens depends on the focal distance and the
image format used. To take an example, the angle of view of a lens with a focal length of 50mm
is about 47°.
The lens opening is the relationship between its useful diameter and its focal length. On most
lenses this is adjustable using an aperture control, graduated on a scale √2p , giving 1, 1.4, 2,
2.8, etc., the lens allowing in more light when the aperture is adjusted to a lower number.
The focusing distance of a lens
Is the distance from the camera at which the subject should give a sharp image on the film.
This distance is linked to the camera’s tirage, the distance separating the optical centre from the
film plane, by the equation:
1/p + 1/p’ = 1 / f
p being the focusing, p' the tirage, f the focal length.
Depth of field of a lens
Is the distance range around the focusing distance, within which subjects found give an
acceptably sharp image. The depth of field is therefore larger as the focusing distance approaches
infinity and the aperture is more closed (higher value).
Is in reality the time during which the mechanism, the shutter, allows rays of light coming
from the subject to fall on the film or on the sensors. It is called a synchronized shutter if it
operates a mechanism to close an electrical circuit, intended to fire a flash, so that the flash will
be optimal while the shutter is open. Some shutters are placed in the centre of the lens and
expose the film and the CCD at the same time; others employ a slot which passes in front of the
film (focal plane shutter) and expose the film and the sensor by scanning.
5 Reminder of Optical elements
in photography
Feature of a lens:
Coefficient of transmission in a medium: Density
When light passes through a transparent medium, it loses some of its energy. This loss is
expressed in terms of coefficient of transmission, which varies as a function of the wavelength of
the light and the medium itself. It is possible to measure this coefficient by measuring the quantity
of light entering and leaving the medium, for example using a light meter:
T = E2/E1
E2
and E1 are the light flows measured at the entrance and the exit of the medium. Such
measurements do not take into account the wavelength of the light. It is preferable to use special
instruments, radiometers, which measure the coefficient of transmission for each wavelength.
The coefficient of absorption is the opposite of the coefficient of transmission; it is known as
the opaqueness.
The idea most currently in use is that of optic density. This corresponds to the decimal
logarithm of the opaqueness.
This is how a medium with an optic density of 0.3 will allow only half of the source light to
pass: a density of 1, 1/10 of the source light, etc. We also talk about the density as a function of
the wave length, Dλ , measured with a spectrophotometer for each wave length in the visible
spectrum.
In a homogenous medium, if we know the density of a unit of thickness of the medium (e.g.
1 meter), we can calculate the density of any thickness of the same medium by multiplying the
unit density by the number of units.
Light reflection:
When a ray of light falls on an opaque object it can be totally reflected following an angle of
reflection symmetric with the angle of incidence with the perpendicular of the subject (specular
reflection), or it can be reflected in an infinite number of directions in a hemisphere centered on
the incident ray, the energy being distributed in the hemisphere equally in all directions (totally
distributed reflection). The reflection can equally be a combination of these two.
There can also be absorption of the rays generally as a function of the wavelength Light
diffusion:
Light difusion:
In a perfectly homogenous transparent medium, light follows a straight line, without being
diverted or reflected. The illumination of a subject situated in this medium is therefore due, if the
light source is unique and specific, to this light source. In realty, no medium is perfectly
homogenous since they all demonstrate sensitive variations of their refractive index and often
contain opaque particles in suspension. Due to the variations in their refraction, the light no
longer follows a straight line but takes a succession of broken paths, sometimes, due to the
suspended particles, the light may be diffused with each particle acting as a secondary light
source. A subject in this medium is no longer illuminated by a single light source, but by an
infinity of secondary sources; on the other hand, the multiple refraction means that even the
direct light from the unique main source does not arrive by a unique path but from an infinity of
directions.
Diffusion by particles
(Legendes)
Particle / particules
Incident ray / Rayon incident
Rays resulting from diffusion / Rayonnements issus de la difusion
What is true for the illumination of a subject is equally true for each of the rays of light
coming from the subject and destined for the observer. The result is first of all a loss in contrast in
the lighting, the subject’s shadows lose their value since the light is dispersed in an infinity of
directions; and there is also a major loss of contrast of the image, the illuminated particles are
between the observer and the subject and form a veil which is much bigger than the distance
which separates the observer from the subject. This is a phenomenon already observed in land
photography during a mist.
The variations in the ray paths surrounding the image will have, as we shall see, a bad effect
on the definition of the subject, particularly the rendition of small details. These notions are not
specific to underwater photography: diffusion can be observed whenever there is mist or fog, even
when it is dry it gives an atmospheric veil; the refractive index of the air varying with the
temperature, and thus its density, as frequently observed at ground level in fine weather when it
can give rise to total reflection phenomena (mirages).
Amongst the particles which may diffuse the light we can equally include molecules of the
material making up the medium. Since these molecules will be dimensionally very small, even
considering their wavelengths, diffusion due to this specific phenomenon will be very weak, and
very variable with respect to wavelengths. It is for a similar type of reason (diffusion of the light
by oxygen molecules) that the sky appears to be blue in land vision. All proportions aside, and as
long as the paths are sufficiently long, we can see diffusion due to water molecules, with a rapid
diminution due to the coefficient of diffusion, when we approach the longer wavelengths (red).
The significance of this “molecular” diffusion is practically negligible with regard to diffusion due
to organic particles and, above all, to instantaneous variation in the refractive index.
6 Application of optical laws to
the underwater medium
Micro refration:
The underwater medium is not a homogenous medium. Wide variations in salinity and
temperature, constantly varying in position with water movement, bring small variations in
density. Minute variations in pressure due to the phenomenon of cavitation, still due to water
movement, cause the spontaneous formation of gaseous nuclei from the dissolved gas. All these
elements join to make the underwater medium a medium with a refractive index that varies
widely from one point to another, the value of 1.33 being merely an average of all these
variations.
Microrefraction
(Legendes)
Dioptres due to differences in the density of the medium.
Under these conditions, a ray of light will not take a straight path except in a purely statistical
sense, following a path that is in fact a collection of broken lines with small variations. This will
give rise to considerable diffusion with, amongst others, the effect of total reflection on moving
interfaces of water of different salinity or on gas nuclei, which makes it impossible to record small
details (compared with the subject/observer distance), implying a small angle between two points
on the subject observed (the angulation of each ray relative to a reference point being marred by
an error which moves and varies according to the conditions of observation).
Apart from the variations in the index of the water medium itself, we should note of life,
which can be considered as transparent but with refractive indices slightly different to water,
which cause the same effects. It is possible to calculate the effect of micro refraction and diffusion
by unit of length of the medium. For a given length, the effect increases exponentially following
the formula
K = K0 10d
K0 is the effect by unit of length and d the distance travelled by the ray.
We understand that under these conditions the lighting contrast falls off very quickly with
depth, stabilizing at a very low level, and that the subject contrast reduces quickly with increasing
distance from the subject to the observer, tending towards 0. In practical terms, underwater
photography is severely limited for these reasons to subjects which are closer as the water’s
coefficient of diffusion increases. This coefficient varies essentially according to the matter in
suspension, from the order of microns up to organic matter (plankton), mineral matter and, to a
smaller measure, gaseous nuclei (swell and waves at shallow depths). Light absorption
Water’s unit density (optic density by meter) varies considerably with the wavelength and with
the matter in suspension. It is in the 500 nanometre band, about 0.013 for distilled water and
0.022 for the clearest oceanic water, the band, which includes the blue/green, considered the
least attenuated. In the 650 nanometre band (red), the unit density reaches 0.2 for distilled
water (energy reduced to almost half at 1 meter) to 0.69 for Atlantic water (energy reduced to
1/5 at 1 meter).
The ultraviolet and infrared rays are immediately neutralized by the phenomena of
resonance within the water molecules. It is the same for the neighboring wavelength bands, with
an effect that is at its minimum in the blue-green. Absorption should be understood as a
disappearance of photons constituting the light energy: it is just one of the causes of the falling
off of light with depth, the other being the changing in path, which is diffusion.
The reduction of light is thus not even across the spectrum and is translated, in the visible
part of the spectrum, into the rapid disappearance of the red rays, then orange, then yellow – the
blue and green persisting to much greater depths. We should note that the notion of depth
should not be considered the only cause of the variation in lighting: we should see the total effect
of the light path; for example, for a subject lit by natural light, the depth, on the one part, then
the distance separating it from the operator. In the same way, when using a flash, we should think
of the path of the light from the flash to the subject and then to the an attenuation of 0.6 (in
very clear water), the energy returning to the camera having fallen to a quarter of its initial
value. It is important to remember these values when photographing underwater in color.
To fix these ideas, here is a table showing the residual values of the light in the blue band
(500 nm) and the red band (650 nm), in Mediterranean type water, at different depths.
Table showing the residual values of the light in the blue band (500 nm) and the red band
(650 nm), in Mediterranean type water, at different depth
Depth
Optic Unit Density
Surface
10 m
Blue
0.08
Red
0.23
100
1.00
16
0.5
20 m
2.5
0.0025
30 m
0.4
0.0000125
50 m
0.01
0.000000063
In the clearest waters, the energy loss is less spectacular; about 10% of the surface energy
still remaining at 56m, 1% at 112m and 1 0/00 at 170m, these being the figures for the blue/
green band. Depending on the suspended matter, the intense diffusion in the blue can absorb the
blue rays more quickly, making the band transmitted slide toward the green (in the case of the
Atlantic coast).
7 Characteristics of natural
light
Light:
We can deduce from the consequences of refraction that light arrives on the subject almost
vertically, since it has a maximum angle to the vertical of 48°. In fact, these conditions are even
more difficult, because a non-negligible part of the sun’s rays are reflected by the sea’s surface.
However, we can consider that 90% of the natural light penetrates the surface if the incident
angle is greater than 65° on the air side, which gives a maximum incident angle in the water
for this value of about 43°. For incident angles of less than 65°, the quantity of light effectively
refracted in the water falls radically if the surface is perfectly flat, which is rare. In fact, we should
not neglect the influence of the waves, which continually vary their incident angles with the
surface interface. The illumination at a point in the water is therefore not due to a ray
penetrating a flat interface, but to the sum of a quantity of rays penetrating a quantity of moving
interfaces. At the limit, bearing in mind the different paths followed by several rays to arrive at
the same point in these conditions, we can see some colored phenomena resulting from these
interferences. If the wave influence is not sufficient to significantly change the angle of
illumination on a subject submerged at depth, it is sufficient to allow a non-negligible quantity of
light to penetrate into the liquid medium, even very high incident angles.
The fact that at depth we have very vertical lighting means that, in spite of the intense
diffusion of this light, the lighting is unsuitable for most subjects, losing detail in the lower parts.
It is therefore necessary in such a case to resort to extra lighting to light these shaded zones.
When light penetrates at an angle other than normal, its effect is reduced, since
a part of the light is reflected.
8 Image contrast
Light:
Visible light can be made up of a collection of different shades, the details of an image being
determined by the difference between these shades and, more precisely, by the relationship of
these shades to each other. It is this relationship which we call image contrast. In the specific case
of an immersed image we distinguish two types of contrast:
a) the contrast made between a subject taken globally and its environment
b) the contrast made between different points on the immersed subject
Contrast of a subject in relation to the medium
The subject’s shade L8 and the environment’s shade LO
The image contrast is defined by the formula:
C=
L 8 - LO
--------LO
Taking into account what we have previously seen, we know that the shade LO depends on
the diffusion of the light in the medium, and is relatively constant for a given type of water and a
given depth. To understand this phenomenon we just have to think of a fog on land. As long as
the thickness of the water is sufficient, the shade at a point in the medium will be the sum of the
shades of all the points in this medium situated along the same axis relative to the observer.
The subject shade L8 depends on several factors:
The subject’s own lighting, a function of the depth and the water absorption, the angle of
lighting of the subject relative to the observer, and its coefficient of diffused reflection k8
thus:
LS = E. k8. cos θ
θ
being the angle between the direction of the lighting and the subject plane, E the lighting
(in lux) at the subject’s level
In the case of a sphere-like subject, we can take θ as lighting angle/observation axis, since we
are interested in the shade of the subject in the axis of observation.
From this it arises that the shade of a white subject is much greater for the observer if it falls
within the axis of the light that illuminates it. Paradoxically, it so happens that this is the worst
condition for taking the photo, either with natural light or flash, since the same law is applied to
the particles in suspension, since the factor LO is itself very high. The rule for taking photos
along the lighting axis will only apply if the number of suspended particles between the camera
and the subject is very low, which is specially true in macro-photography where the camera/
subject distance is very small. The shade will not vary by much if the lighting angle is between 0°
and 45° (from E to 0.7 E, is about _ an f stop), so it would be appropriate to use a lighting angle
between the flash and the subject axis of about 30° to 45°, to bring out the relief in the subject,
in short, to “model” it.
This rule is useful not only in macro-photography but also for any close-up photography in
water with a low level of suspended matter.
For larger subjects, taken from a distance of several meters, it is much simpler. We already
know that for all the dark subjects, L8 is weak before LO, the contrast will fall quickly below the
critical perception level (for memory, the limit of value C for visual perception is of the order of
0.02), forbidding the photographing of such subjects in the lighting axis, due to the higher values
LO, it would otherwise be necessary to completely distort these values for this type of subject.
It works differently if there is a big angle between the camera/subject axis and the lighting
axis, say of about 180°, which would become a complete “against the light” shot. The subject
appears dark against a background of suspended particles and becomes detached from the
diffuse lit background. Or, if the depth is shallow and the shooting angle almost vertical, toward
the sky, seen through the surface. In these conditions, L8 is zero, LO maximized around the
subject, but almost zero in the subject axis; the lighting of suspended particles is almost entirely
due to diffusion.
Obviously, the further away we get from the subject, the greater is the diffusion, and it soon
reaches its primitive level. Photography of larger dark subjects will be preferable against the light
and as close as possible, which will require the use of wide-angle lenses. To avoid the silhouette
effect it would be best to light the subject from an angle of 30° or 45° to the subject axis. If we
are photographing in color, we will get better contrast, due to the blue color of LO and the more
violent colors of the subject whose red rays will not be absorbed completely by the short distance
of water. It is also desirable that the underwater participants avoid adding to the natural
suspended matter any additional mud caused by the operators clumsy movements.
Contrast of the interior details of the subject At zero distance from the subject, with no
diffusion or absorption, the subject contrast will correspond to a formula comparable with the
previous case.
If we call L2 the shade of the palest particles and
subject contrast:
L1 that of
the darkest, we will get the
L2 – L1
-------L1
C8 =
But we need to take into account the water’s absorption of the rays coming from the subject.
If D is the optic unit density of the medium and d the observation distance, the subject contrast,
L2 .10 –dD - L 1 . 10 dD
Cs(d)
=
--------------------
L 1 . 10 -dD
The contrast appears to stay the same, since the attenuation plays equally on the high and the
low shades. The introduction of diffusion, the parasite lighting LO, changes everything:
L2 - L 1 - LO,L 1
Cs(d)
=
------------------
LO,. 10 dD
We see that the subject contrast observed from a distance d falls rapidly to 0, and more so if
the medium’s optic unit density is higher. A subject seen from a relatively great distance will lose
all detail as the image contrast is reduced. We have seen previously that the micro-refraction
effect combines with diffusion to amplify this loss of definition. Here again, we see the necessity
to get as close as possible to the subject, using extra lighting so that the contrasts in the volume
are brought out, to once more reinforce the difference between L2 and L1 . The factor LO
always depends on the particulation and the lighting of this particulation, the decision to operate
against the light remains valid if there is strong ambient light.
9 Variation of size of an
apparent focal image
We have seen above that an immersed subject viewed through a flat port appears to be nearer
by 1/4. Obviously, since it appears to be nearer to the observer, it will also appear larger than it
does in air. This apparent magnification is due to the reduction in the field of vision by refraction
when the rays pass from one medium to another. We have already covered the subject of angle of
field and a simple construction will be more useful in showing the effect of varying the angle.
The angle of field is reduced only in the water medium and the eye and the lens continue to
function under normal conditions it follows that the apparent magnification of observed objects
is only an illusion, the eye and the lens translating the perceived image as if it were in air. The
notion of the angle of view is closely linked to the focal length of the lens and, for a given image
format, it is as if the focal length of the lens had been increased, producing a telephoto effect. We
must then adopt the notion of apparent focal length for this new angle of view. We must
underline that this notion is entirely practical and should not be used except with the greatest
precaution, since the focal length of the lens has not changed for any factor other than the angle
of view.
If α is the angle of view of the lens in air and α' its apparent angle in the water, through a
flat port, Descartes law will give us:
α' = 2 arc sin (0,75 sin α / 2)
Thus, for α = 600, α' = 44003' , giving a coefficient of 1.36.
This coefficient varies with the angle of view; for example, for α = 920, α' = 65018', and the
coefficient is 1.41. However, as we rarely use wide-angle lenses with a flat port, we can consider
that the coefficient of the angle of view is close to the refractive index and use, for simplicity, the
coefficient 1.33 for dividing the angle of view and for multiplying the real focal length, to obtain
the apparent focal length. This will be true as long as the original angle of view is of the order of
60° or less.
Under these conditions, we can say that a 50mm lens acts like a 66 mm, or a 35mm
lens acts like a 47 mm.
Field angle
This notion of apparent focal distance can be recalled in another feature of the lens: We have
defined the relationship between the pupil and the relative focal distance, thus:
A=
ω/F
where ω is the diameter of the pupil (defined by the diaphragm) and F the focal length. In
the air-filled part of the housing, the diameter of the pupil stays the same when immersed and
the light energy coming from the subject is distributed over a surface (1,33)2 times bigger, on the
film, than in air. To have the same photographic effect and the same exposure we can increase
the exposure time by the same proportions:
T' = 1,77 T or we can open the diaphragm sufficiently to compensate for the loss of energy,
thus 0.82 diaphragm.
The aperture used will therefore appear smaller when used underwater, in the relation
A' = 0,75 A, it will appear to correspond with the diameter of the pupil divided by the
apparent focal length, thus:
A'= ω
/ F'
This notion of apparent focal length will have an additional impact on the exposure, with the
need to open the diaphragm by one division (exactly 0.82 diaphragm) compared with the light-
meter reading, provided that it is submitted to the same rules. A TTL light-meter, reading
through the lens, will give an exact reading.
On the other hand, the flash exposure will often be made according to a guide number,
obtained by multiplying the diaphragm opening to be used, for a given film, by the flash-subject
distance. For an underwater exposure, we find, that compared with this guide number we need to
open the diaphragm by one more stop, which amounts to dividing it by 1.4. The fact that the
subject is actually further away from the photographer than he estimates (due to the apparent
1.33 magnification) introduces a second multiplication coefficient of (1,33)2 for the exposure
time, once more 0.82 diaphragm. So we will open the camera diaphragm to 1.64 compared
with the indication given by the guide number, which amounts to dividing it by 2. None of this
takes into account the supplements due to the absorption of light by water, and by the diffusion
and loss of light by the parasite reflections on the port, which will vary with the working
conditions.
It should be understood that all the above refers to the use of a housing with a flat port,
which in any case would be rare on professional equipment, but may be more common on the
less sophisticated equipment such as the lower priced housings.
10 Geometric distortion
associated with a flat port
We understand by the term “shooting angle” the angle made by the rays coming from the
extremes parts of the subject. One of these parts being situated on the optical axis, while the
centre of the angle is the optical centre of the lens. We will indicate the shooting angle in air by
the letter β, γ being the corresponding angle in water, produced by β passing through the flat
port of the housing.
Variation of the distortion rate as a percentage with the shooting angle
A subject with a height h, gives an image on the film of height h'.
We call this magnification the value:
G = h'/h
When photographing in air, the magnification is linked to the lens’s focal length F and the
subject distance by the formula
G = F/(d-F)
What we are looking for is the extent to which coefficient G can be affected by the refraction
of the rays coming from the subject as they pass through the flat port. We have already seen, in
the definition of apparent focal length, that the distortion varies with the angle of attack; we still
need to give a value to this distortion.
In water, the shooting angle of a subject of height h at a distance d will be:
γ = arc tg h/d
We know (from Descartes law) that γ and β are related by the formula:
sin β = 1,33 sin γ
The image height h' on the film is given by the formula:
h' = dF/(d-F) x tg β = dg tg β
g being the magnification factor of the optical assembly functioning in air. If
we call h the size of the subject in water, we can define a new magnification
factor g', so that:
g’ = h'/h
From the preceding formulae we find:
We see that the real magnification, the relationship between the dimensions of the subject in
water and the image on the film or the sensor, is a complex function of the shooting angle, and
that the angle will be greater as the angle approaches its limiting angle (48°45'), at which angle
g' becomes infinity. In these conditions, an image of concentric circles, equally spaced, will be a
series of concentric circles spaced wider apart as their diameter increases, their centre being on
the optical axis. In the same way, an image of a square (the shooting angle being greater at the
corners of the square than at the centre of the sides) will no longer remain a square but a
symmetrical geometric form whose distinctive shape gives this type of distortion the name
“cushion distortion” or even “positive distortion”.
The light emitted by a point on the subject is distributed over an even larger surface as the
magnification increases. The exposure will vary inversely with the square of this magnification.
The real aperture A' will vary according to the point on the subject analyzed, A being the
theoretical aperture of the lens, read from the aperture control ring, incorporating various other
secondary factors:
A’ = A / 1,77 cos2 γ
This explains the phenomenon, mostly seen with wide-angle lenses, of an image that is
lighter in the centre than at the edges.
11 Chromatic aberrations
linked to refraction in water
When we speak of the refractive index of transparent media, we should understand “average
of the refractive indices for each wave length in the visible spectrum”. In fact, this index varies in
measurable proportions with the color – wavelength – of the rays in question. To give the reader
an idea, the refractive index of water is 1.343 for the 400 nm wave length (blue), 1.334 for
550nm ‘green) and 1.330 for 700nm (near infra red). The refractive index also depends
(we have already mentioned this) on the water density, including factors such as the salinity, the
temperature and the pressure. So if we examine the refraction of a ray of composite light (white
light) as it leaves the air/water interface, we see that the deviation of the red, orange, yellow, etc.
components of the white light will vary as a function of the color, the blue rays being more
refracted than the reds, with the spectrum spread between these two. This is the phenomenon
known as dispersion.
This dispersion will have great importance in photographic performance: the apparent
distance of a subject being linked to the refractive index, we should talk about the apparent
distance for each color on the subject, since there is up to 1% variation between the blue and
the red. The phenomena of diffusion and micro-refraction are also involved, for the same reason,
the wavelength of the light affected.
It is in the variations in the enlargement factor that the phenomenon is most sensitive. We
give here the enlargement factors g’/g for indices of 1.33 (red radiation) and 1.34 (blue
radiation) for shooting angles of 20° and 45°.
We see that the enlargement factor, due to the refraction through a flat port, varies by 1%
between the red and the blue for a shooting angle of 20° corresponding to a normal lens, to 7.2°
for a very wide angle. This will have the effect of recording images of different sizes
depending on their color, the smallest being the red and the largest being the blue, it being
understood that all complex images contain the sum of all the wavelengths in the spectrum. The
effect is seen as the appearance, principally on the edges of the image where γ is highest, of
colored fringes with a distinct loss of definition in black and white. This defect carries the
name chromatic aberration.
12 Spherical aberration
We have seen that rays coming from a point situated on the optical axis are refracted as they
pass through the port, the rays being refracted further away from the optical axis as their incident
angle increases. Looking at this from the “air” side of the glass port, these rays appear to come
not from an unique point, which would be the virtual image appearing at 0.75 of the real
distance, but rather from a whole family of points, even closer to the port as their angle increases.
This is what allows us to arrive at the preceding reasoning, notably on the variations of the
apparent focal length with the angle of field. The virtual image of a point being a family of
points, and this reasoning is true for any real point, whether on the optical axis or not, we can say
that the image of a subject will not be an unique image but a family of images, at different rates
of magnification, translating the subject into a blurred total image. This phenomenon, known as
spherical aberration, becomes more sensitive with increasing angle of field and opening of the
aperture.
Here we can see the reason not to use a flat port with a wide-angle lens, plus the
recommendation to use as small as possible an aperture. We can now list the various kinds of
aberration likely to degrade the image quality when photographing underwater with a flat port:
astigmatism and coma, the principal ones, find their origins in the differences in the path taken
by rays coming from the subject in a plane including the optical axis, compared with rays situated
on a plane which does not include the optical axis: so the image of a cross which is not situated
on the optical axis will be situated on two different image planes (implying two different focus
points), one where the horizontal branch of the cross is sharp, the other where the vertical (radial)
branch is sharp. This defect is more marked as the aperture is opened. All of the optical defects
mentioned can be seen by the observer through his mask, as it is effectively a flat port, as long as
he is looking out for them.
Meanwhile, the eye’s field of view is relatively narrow and the line of sight usually
perpendicular to the plane of the mask, so they may not appear very obvious. When examining
photographs, the most obvious defects are those due to chromatic aberration, when the fringes
are clearly visible, and spherical aberration, when the image is blurred at the edges.
The defects of a geometric nature (distortions) are generally less clear, due to the nature of
the subjects photographed. These should then be examined more seriously if we want to
reproduce the subject correctly, usually by
13 The principle of aberration
correction
Although it is possible, as we have already mentioned, to do good work with a flat port, in
spite of the many aberrations they can bring (and as shown by the numerous images made with
small and disposable cameras), it is obvious that if we are aiming at higher quality results, mainly
by using wide-angle lenses, then we will need to correct the aberrations which can begin to
become troublesome with this type of lens.
The characteristics which often make a photograph taken with a flat port easy to recognize
are the washed-out colors and its soft point. The principle normally followed to correct the
optical aberrations consists of completing the lens by adding an additional element that has the
same aberrations, but in the opposite sense.
The focal length resulting form the joining of the two lenses with focal lengths respectively Fl
et F2, separated by the distance d, is:
In selecting the elements of these lenses, with very different characteristics of refraction,
dispersion, etc., we tend to create systems having acceptable convergence but having no
distortion (orthoscopic), nor spherical aberration (aplanetic), nor chromatic aberration
(apochromatic), nor astigmatism (anastigmatic).
The principles long applied in the correction of lenses traditionally used for land
photography can be used in the case of underwater photography, to correct the aberrations that
we have mentioned. However, the application is simplified in the sense that we do not attempt to
correct the main lens itself, which is usually quite acceptable, but only the aberrations known to
be due to the flat port.
Correction of the distortion produced by a flat port.
This correction could be made using a plano-concave (divergent) lens, with an appropriate
curve and index, giving a negative distortion (barrel) the inverse of that given by the flat port.
This lens can be mounted on the main lens, on the port, or can even constitute the port itself.
Correction of chromatic aberration
This correction will be made by making a port with two lenses, one plano-convexe
(convergente) and a plano-concave (divergent), contiguous, both made the same refractive lenses
(combination being infinity) but with different dispersion, so that the opposite defect to that of
the original lens is produced.
14 Correction systems
1- Dome ports
The first type of corrective port is to not use a flat port at all, but a hemispherical port, of
appropriate radius, centered on the optical centre of the lens used. The radius of the port is
selected in relation to a specific lens, so that all rays coming from the subject converge at the
optical centre having passed through the port normally, that is to say perpendicularly to the
tangent plane at the point of entry. In these conditions, the ray is always perpendicular to the
interface whatever its angle of incidence, and is never refracted. Such a port will not, therefore,
introduce any distortion, and the lens’ nominal field of view is maintained, with the reservation
that the port, having one water face and one air face, acts like a spherical lens so that we can
calculate the focal length on the air side and the water side with the following formula:
a general formula, where n is the index of refraction of the glass used, R1 and R2 the radius
of curvature of the two faces of the lens.
This formula should be applied to our case by assuming the port is a plano-concave lens with
an index of 1.33.
The focal length in air is thus:
and the focal length in water is:
The dome port acts as a divergent lens. It is necessary to correct this divergent lens with a
convergent lens of the same power with a focal length of 4R or, if preferred, a power of 4R
dioptres. If we know R, it is easy to find a suitable lens in the shops, which can then just be
screwed on to the main lens like a hood.
There are also correction systems. This hood can if necessary be omitted, the the lens should
be focused at a distance of 4R (opposite case of a close up lens), which can usually be achieved
without problem.
But, as is often the case with bottom-of-the-range cameras, adjusting the focusing requires
modifying the optical characteristics of the lens, such as fixing the position of the optical centre
within the housing. Since the camera usually has a fixed position in the housing, as has the port,
the main condition for eliminating the effects of refraction, that the port is aligned with the
optical centre of the lens, cannot be achieved.
Fortunately, since the invention on all quality lenses of internal adjustment without moving
the optical centre, this inconvenience no longer needs to be taken into account and the main
condition for eliminating the effects of refraction, centering the port with the optical centre, can
be met.
On the other hand, there is no question of using a zoom lens, due to the same factor of
moving the optical centre. Dome ports, although more expensive than flat ports, offer an
economical means of correcting aberrations on underwater photographs. They are typically
made of relatively thin glass or acrylic, and although they have a shape that is well adapted to
resist pressure, they can be fragile where knocks are concerned. In any case, they represent the
only economical solution for working with wide angle lenses that have an angle of view greater
than 90°.
The major inconvenience of this system is that it generates a virtual image that is positioned a
few centimetres in front of the port, and this requires the use of a fixed focal length lens used in
the macro position. Certain zooms, such as those used in DV cameras have a cover of no more
than _ inch and have a slight displacement of their optical centre which may be acceptable with
a dome port whose radius is carefully calculated to be between the two extreme positions of the
optical centre at its focal length limits. But it still remains rare to find a dome port that will accept
all the camera’s focal lengths except with correction using an aspherical port.
2- Magnification Correction:
Ivanoff-Rebikoff System
The problem is to correct the magnification of 1.33. This correction can be made by
completing the lens with an afocal system giving a magnification of 0.75, comparable with the
optical supplementary lenses like the HyperCinor type. Such systems are like a reversed Galileo
lens and are made up of a divergent lens with a focal length of Fn, completed with a convergent
lens with a focal length of Fp, these lens being separated by a distance d. The
system is afocal when:
Fp + Fn = d (focal lengths in algebraic values)
The magnification factor is:
g“ = Fn / Fp
The condition is satisfied when: Fn = 0,75 Fp
The Ivanoff adaptor uses such a system, which has a negative distortion that
balances the distortion of flat ports, complemented by a strong chromatic
correction, obtained by using pairs of lenses for each element, made of glass
carefully selected for its dispersion powers.
Magnification Correction: Ivanoff-Rebikoff System
This system, in which the port itself constitutes the plano-concave element, is almost the
absolute weapon of the underwater photographer. It allows the use of all types of standard
lenses, restoring their focal lengths and their angle of field while correcting all of the typical
aberrations associated with a flat port.
The great thickness of the elements makes them very robust and resistant to both knocks and
pressure, with the only point against the system being its relatively high price.
In the preceding demonstrations we did not take into account the thickness and the refractive
index of the port itself. On the one hand, the port has a low thickness compared with the lenssubject distance, and on the other hand the refractive index of the glass used in such ports is close
to that of water (1.5 for the glass). We can, at the limit, ignore the glass’s own dispersion effects,
just considering it as an additional thickness of water.
In practical terms and even with fairly precise calculation, it is possible to ignore it completely
without major problems.
3- Corrections based on aspheric ports:
It's a Swiss engineer optician François Laurent, who at the request of Luc Besson for his film
in CinemaScope "THE BIG BLUE" tackled the particularly complex problems of underwater
correction for the CinemaScope lenses and zooms. François Laurent found solutions based on his
optical engineering and the calculating power of modern computers. He created a series of
Thalacétor correctors, systems based on the application of optical laws using the properties of
aspheric surfaces.
Correcteur Asphérique THALACETOR