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The Mathematics of Depth of Field (DoF)
Depth of Field (DOF)
Depth of field is the distance between two planes, a closer one and a farther one, in which objects can be positioned to have an "acceptably sharp" image formed in a camera.
There are two formulae for calculating Depth of Field (DOF), a simple one as described below which produces an approximate value and more a more complicated one which produces a more accurate value. The latter is not discussed in this document.
I will focus on the simple formula as below.
DOF = (2 u2 N c)/f2
*circle of confusion has been defined as the largest blur circle that will be perceived by the human eye as a point when viewed at a distance of 25cm. Note there are more specific definitions but for the purposes of this document the above definition is considered sufficient.
The formula shows that DOF varies proportionally with the aperture, and with the square of the focal length and distance to subject.
Example: what is the DOF of a 50mm lens, when the circle of confusion is 0.029mm, f-stop is f/4 or 4 for the calculation, with a focus distance of 1200mm (1.2m)
Answer: square of u = 1200 * 1200 = 1,440,000
So DOF = 1,440,000*2*4*0.029 = 334,080 divided by square of focal length = 50 *50 = 2500
Ie 334,080/2500 = 133.632mm = 0.13m
An example of Camera "Back Button Focus"
In late 2020 my Camera Club held a "Show & Tell " session where members had to present 12 photographs taken from the same place.
The full sequence of 12 photographs can be viewed at: https://www.hmphotographs.com/p878971621
First Event of 2023
First Event if 2023
My first event if 2023 was horse racing at Down Royal. The event was the Molson Coors Raceday national hunt meeting. It was also Students’ Day and was noisy. There were three hurdle races , three steeplechase races and a flat race to complete the meeting. The meeting was the only one in the UK and Ireland on the day so got good coverage on Racing UK TV. The weather was good considering it was January- dry and bright and not too cold for most if the afternoon. I took photographs with 24-70 and 70-200mm lenses on both sides of course at the the last hurdle and fence as well as some at the finish. I had 5 photographs published in a weekly newspaper. Photographs from the day can be viewed at gallery https://www.hmphotographs.com/p193199369
A Day at the Races
As of March 2022 I have attended and photographed 270 horse race meetings. I thought it would be interesting to document the things I do for each meeting in terms of pre-meeting, at the meeting and post meeting activities. I have attached a chart detailing these activities.
Top viewed photograph in 2022
This is the top viewed photograph on my site in 2022. The list is at: https://www.hmphotographs.com/p189364346
I took it at the GRE Games at the Antrim Forum in Northern Ireland in 1982 and shows Stephen Metcalfe jumping in the long, ship and jump comptetition.
Camera Club Zoom Talk in October 2020
Rory McIlroy after breaking the course record at Royal Portrush in 2005
I presented this slide set to Larne Camera Club members via Zoom on Tuesday 13th October 2020.
hmphotographs | 2020-10-08th-Camera Club Slide set V1
Where to Stand?
The photograph below is of the 2010 JNWine Champion Chase at Down Royal and shows Killyglen ridden by Paul Carberry on the left and Kauto Star ridden by Ruby Walsh in the right. Killyglen was owned by David McCammond of Killyglen and trained by Stuart Crawford at Magheramourne near Larne in County Antrim, N Ireland and finished 5th in the race. Kauto Star, winner of the race was trained by Paul Nicholls from England.
Collection of Photographs of Champion Race at Down Royal referred to below: hmphotographs | 2023-01-06th-Where to Stand?
Ansel Adams states that “A good photograph is knowing where to stand” and best selling author Tom Ang states in one of his books “The essential foundation for every image you make is your choice of viewpoint”
At each event I attend the most difficult decision I make is usually where to stand. I have attended the same events on many occasions and struggle with this decision each time.
I will state at the outset that my objectives in taking horse racing sports photographs are to capture action pictures of horses galloping and jumping as well as interesting photographs recording the events such that parties involved with a horse will consider buying a print or jpg file and newspapers editors will consider publishing in the sports section of their newspapers.
In most races at Down Royal the horses and riders pass you two times if you stand in the correct place so you get two bites of the cherry. I usually photograph from the same place on both circuits but I have moved from the last fence to nearer the finish for the second circuit to be able to get to the winners closure in time.
At Down Royal the direction of the light is not usually a problem as the horses run towards the light at the last fence and the finish. Backgrounds are a problem as there are car and bus parks near the last fence and overhead electric power lines and poles near the finish.
There are a number of viewpoints at Down Royal and it is tempting to try to summarise where I stood for each of the 728 races photographed. I may attempt this analysis in the future however for the purposes of this exercise I have considered one race which I have photographed 12 times. This is the Grade 1 Champion Steeplechase which is held at the two day festival of racing in early November each year.
It is a major National Hunt Race in the UK and Ireland Racing calendar and it attracts the best horses, owners and jockeys as well as the top sports photographers from across Ireland. A National Hunt race means the race includes fences. Where to Stand for Flat races poses different questions than jumps races.
I photograph a horse race at Down Royal from a number of locations ie parade ring, leaving the parade ring, going down to the start, running on the course, jumping - usually the last fence, running up the finishing straight, crossing the finishing line, entering the winner’s enclosure and in the winners enclosure.
The photographs which cause me most indecision are:
- running up the finishing straight and
In each case you can stand on the horses’ left or right side as they run to the finish line.
At the last fence there is also the option of standing on a ladder which can get you above spectators and/or provide more of the horse as it jumps the fence.
I have compiled a collection of photographs from the galleries of the 12 races to demonstrate where I have stood for the various races. I have also included photographs taken in the parade ring, leaving the parade ring, going to the start and entering the winners enclosure and in the winners enclosure. Where to stand is less of a problem for these photographs because they were mostly staged and arranged or are random shots. Problems arose though if the groups were standing with their backs to the sun and a flash unit was needed in those circumstances.
I have listed below the various races attended by year, winning horse name and in each case which side of the course I photographed the horses jumping the last fence or running up the finishing straight. I have also indicated when I used a ladder at the last fence. The ladder allows the photographer to get above spectators heads and also provides for a fuller view of the horse as it jumps the fence.
Factors that affected the decision as to which side to stand:
1 It was easier to get to the winners Enclosure from the left hand side before horses returned to the winners enclosure
2 The location of the last fence also affected whether the last fence was the chosen – the further away the last fence was from the finish line the longer it took to get to the winners enclosure.
3 The location of the last fence also affected the background – some locations on both sides had cars and buses showing
4 In the 2010 Kauto Star Race a fence past the finishing post was chosen which had the Grandstand in the background. It was not possible to get to the last fence for the final circuit so photographs were taken from the run-in near the finish.
5 The last 4 races were photographed from the left side using a ladder primarily because it was possible to get to the winners enclosure in time to photograph the winning representatives. The ladder also improved the background.
6 I have photographed this race from the left hand side of the course on 8 occasions compared to 4 on the right primarily because of the ease of getting to the winner's enclosure on time.
7 My preference is to photograph from the right hand side of the course as the horses run to the finish as for 2015 Don Cossack and 2016 Valseur Lido. The background is better if the fence is positioned in a certain place at the final fence when the photographs were taken from a kneeling position. On the run-in to the finish it is possible to get the spectators in the photograph which adds to the atmosphere.
8 The photograph shown above of the 2010 Race showing Kauto Star jumping was taken at a fence beyond the finish on the left hand side of the course and is probably my favourite of all photographs taken of the race, mainly because it is of Kauto Star, a very famous race horse but also because the horse on the inside (Killyglen) was a locally owned and trained horse. Also I liked the fence location, the background of the grandstand and the direction of the light. I only shot from this position once because the horses only passed once and it was not possible to get to the last fence on time.
Mountain Runnng Events
Between 2005 and 2017 I photographed 43 Mountain Running events in Northern Ireland. There were mostly in the Mourne Mountain.
I have over 10,000 photographs in my gallery - https://www.hmphotographs.com/f691398371
Mountain Running is organised in Northern Ireland by the Northern Ireland Mountain Running Association (NIMRA) and the two Athletics Clubs most involved are based in Newcastle- Newcastle AC and Mourne Runners.
The same races are run every year which provided the opportunity to photograph the races from different locations.
Some of the races I have photographed are as follows:
- British Championships: 2017, 2013, 2012, 2011, 2010, 2009 2008,2007
- Lurig Mountain Race in Cushendall - 2011, 2010, 2008, 2007,2006
- Race over The Glens - 2015, 2014, 2012, 2011, 2010, 2008, 2007
- Sevens Sevens in The Mourne Mountains - 2010, 2009, 2007
- P&O Irish Sea International Mountain Race at Knockdhu - 2006
- World Police and Fire Games including the Mountain Race in the Mourne Mountains -
Horse Race Meetings attended
I have over 50,000 photographs loaded in my Horse Racing galleries on my site and so I though I would count the number of meetings I have attended over the years.
As of March 2022 I have attended 270 meetings which equates to photographing 1,754 races - a track meeting normally has 7 races and a Point to Point meeting has normally 6 races - though sometimes if there are two many entries in a race it is divided into what is called into a Division 1 and a Division 2 race. I was once at an East Antrim Hunt Point to Point Meeting at Loughanmore, near Templepatrick where 11 races were run.
I have attached a spreadsheet showing the horse racing venues I have attended.
My Web Site Configuration
There are many ways to configure a web site.
I set up my first sports photography web site in 2006 and have been using Zenfolio since 2010.
IN early 2010 I decided to set up Zenfolio by type of sport ie all photographs for a particular sport in a collection of galleries eg Cross Country Running, Mountina Racing, INdooor Athletice etc.
I created a gallery for each event I attended.
When you enter my site you will be presented with galleries for each sport eg Horse Racing, Golf, Mountain Running, motor Cycle Racing, Sailing, Rugby, International Cross Country, indoor Ayhletics, Hockey, General Sports and some other ad- hoc galleries.
If you select Horse Racing you will be presented with the Horse Racing tracks I have attended and within each of the tracks I have grouped the photographs by meetings in each year.
In Zenfolio photographs are uploaded into Galleries. Galleries can be combined into Groups of Galleries to many levels. Zenfolio also has a Collection facility which contains a pointer to selected photographs in their Galleries. This means that the original photograph is only stored once in the system.
In order to allow the viewer an alternative way into the galleries of photographs I have created an index by year from “2005 and earlier” up to the “current year”. Within each year I have listed each event attended with a pointer to the gallery containing the photographs of the event.
Zenfolio also has a blog facility and I have included items which interest me mostly related to the events I have attended.
Zenfolio gas a “Customs Page “ facility which I have used to create an index to my blog which shows a heading for the log entry and a pointer to the blog details.
Zenfolio has many different front page styles and format for displaying sites. I have selected a basic format where I have selected a number of featured galleries followed folllowed by Galleries recently posted with finally the galleries in my site.
Changes at Down Royal in 2018.
The picture above shows Kauto Star and Ruby Walsh winning the JNWine Champion Chase at Down Royal in 2010.
The last meeting at Down Royal Racecourse , arranged by the Down Royal Corporation of Horse Breeders was held on on Boxing Day 2018. The Corporation had run race meeting for 35 years at the course but the lease was not renewed by owner of the Course Mike Roden of Dublin based Merrion Property Group who purchased the site in 2005.
Racing has continued at the Course organised by new owners Merrion Group.
I have taken photographs at the site since 2010 and thought it be appropriate to create some collections of photographs under different headings of photographs I have taken at the course.
The photographs can be viewed at: https://www.hmphotographs.com/f400896471
Show and Tell - "I know what you did last autumn"
My Camera Club held a Show and Tell on Tuesday 11th January 2022. The subject was show and tell up to 6 photographs on the topic "I know what you did last autumn".
I submitted 6 photographs as shown at the attached link taken at the second day of the two day race meeting at Down Royal on Friday 29th and Saturday 30th October 2022 - https://www.hmphotographs.com/p453452691
This is a significant racing weekend in Irish Racing with total prize money ofer the two days of 405,500 Euro - 144,500 Euros on Friday and 261,000 Euros on Saturday.
The Golden Rectangle
The Golden Rectangle (See pictures at: https://www.hmphotographs.com/p113904293 }
The Golden Rectangle is a rectangle where the dimensions adhere to the Golden Ratio ie the ratio of the width and height is 1.618.
For example if the height is say 10” then the width will be 16.18” (10 times the Golden Ratio of 1.618)
Interestingly the Golden Rectangle can be split into a square with a vertical rectangle at the end (Picture 1). This vertical rectangle also has the dimensions of a Golden Rectangle which can be split into a square and rectangle at the top or bottom and again the new rectangle is a Golden Rectangle and so on. This is the basis of the Golden Spiral.
Back to the original rectangle (Picture 1 ) discussed and the square and vertical rectangle at the end. The vertical rectangle if rotated 90 degrees anti-clockwise fits into the bottom left of the square (Picture 2). It will also fit the bottom right part of the square drawn for the right of the overall rectangle (Picture 3 ). This also applies to the mirror image of the original rectangle where the square is at the right side of the rectangle (Picture 4).
The end result is a Noughts and Crosses shape which is similar to the Rule of Thirds shape with the four focal points (Picture 4 ). Note in Picture 5 the Golden Rectangle is represented in Blue and the Rule of Thirds in Green
I have seen it said that the Rule of Thirds is based on the Golden Rectangle and that the Golden Rectangle focal points are more effective from an atheistic point of view than those in the Rule of Thirds.
The other interesting feature of the Golden Rectangle is the closeness of the shape (1.618 ratio) to the 35mm wide film ratio ( 36mm by 24mm = 1.50 ratio) and the modern full frame camera sensor ( 36mm by 24mm = 1.5 ratio)
There are many architects, artists and photographers who have made use of the Golden Rectangle in their work.
The Golden Ratio
The mathematics of the F-stop numbers
Have you ever wondered where the camera f-stop range of numbers comes from ie 1.4, 2, 2.8,4,5.6,8,11,16.
Well it is fairly simple.
The number sequence is related to the area of a circle and the fact that the difference between 2 full f-stops doubles or halves the amount of light that gets through the aperature ie the area of the circle doubles or halves.
It turns out that if you multiply the preceding number by the square root of 2 ie 1.414 (to three decimal places) you get the next number in the sequence ie 1.4 multiplied by 1.414 = 1.9796 or rounded up =2 or 2 multiplied by 1.414= 2.828.or 2.8 rounded to one decimal place.
It is also interesting that the number either side of a number is either double of half ie 2 and 4, or 16 and 8
I have written out the mathematics explaining the relationship between the numbers and where the square root of 2 comes from.
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