MTF and "The Sharper Image" - What matters most ?

Started Jan 30, 2012 | Discussions
Detail Man
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MTF and "The Sharper Image" - What matters most ?
Jan 30, 2012

"The Pinhole Camera Revisited or The Revenge of the Simple-Minded Engineer" is quite interesting:

http://www.biox.kth.se/kjellinternet/Pinhole.pdf

Check out the "Pinhole Camera MTF (modulation transfer function)" graph, and check out the simulated images that follow in the referenced paper. The gist of it (as stated in the paper) is that:

In order to produce a sharp-looking image, the imaging system must have high MTF values at low and medium-high frequencies. MTF curves that drop rapidly as the spatial frequency increases will produce fuzzy-looking images, even if they extend out to high spatial frequencies .

I thought that some readers might find the paper to be thought provoking in relation to conceptual assumptions that a MTF that extends to higher absolute spatial-frequencies necessarily equates to the visual perception of a "sharper image". The images in this paper appear to demonstrate otherwise - and indicate that human visual perception in this respect is not as simple as "more is better" (where it comes to merely assessing the maximum spatial-frequency response).

This human visual perceptual phenomenon may have some relevance to recent discussions here ...

If nothing else, the cartoon of the "simple minded engineer" kicking the "able bodied engineer" squarely in the ass may likely appeal, and bring pleasure, to many who are suspicious of numbers !!!

If you don't happen to find this referenced paper and post interesting, there are plenty of others .

DM ...

MAubrey
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jan 30, 2012

That was excellent. Thanks for sharing!

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dotborg
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jan 30, 2012

I guess that's why some lenses don't necessarily have the best MTF but still appear sharp.

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to dotborg, Jan 30, 2012

dotborg wrote:

I guess that's why some lenses don't necessarily have the best MTF but still appear sharp.

(Based on the points that the paper makes), I wonder if the integral (area under the curve) of the MTF at any given spatial frequency may possibly tell more than the magnitude of the MTF itself ?

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jan 30, 2012

This is the kind of stuff that very likely (more so than a simple integral of the MTF function) correlates best with human perception (nothing new, but not something that I know a lot about):

http://www.imatest.com/docs/sqf/#csf

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dotborg
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jan 30, 2012

Detail Man wrote:

This is the kind of stuff that very likely (more so than a simple integral of the MTF function) correlates best with human perception (nothing new, but not something that I know a lot about):

http://www.imatest.com/docs/sqf/#csf

Interesting. Thanks for the link.

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jan 30, 2012

Bob Atkins has a somewhat more "streamlined" write-up about SQF here:

http://www.bobatkins.com/photography/technical/mtf/mtf4.html

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jan 30, 2012

Dig this :

... the subjective sharpness of a print corresponds to the area under the MTF curve between the spatial frequencies of (0.5 x magnification) and (2 x magnification) when spatial frequency is plotted on a logarithmic scale .

... if we make an 8x10 (or 8x12) print from a 35mm negative we have to magnify the negative by a factor of 8 (since the negative is approximately 1" x 1.5"). So as far as the SQF is concerned, the area under the MTF curve of the lens between 4 and 16 cycles/mm is then what really counts .

http://www.bobatkins.com/photography/technical/mtf/mtf4.html

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Feb 1, 2012

Detail Man wrote:

... the subjective sharpness of a print corresponds to the area under the MTF curve between the spatial frequencies of (0.5 x magnification) and (2 x magnification) when spatial frequency is plotted on a logarithmic scale .

... if we make an 8x10 (or 8x12) print from a 35mm negative we have to magnify the negative by a factor of 8 (since the negative is approximately 1" x 1.5"). So as far as the SQF is concerned, the area under the MTF curve of the lens between 4 and 16 cycles/mm is then what really counts .

http://www.bobatkins.com/photography/technical/mtf/mtf4.html

I am beginning to think that spatial frequency resolving abilities of human visual perception just might have a fair bit to do with why stopping-down to F-Numbers higher than 2.0 (at 700nM, with pixel-pitches on the order of 4.0 Microns on M43 image-sensors) appears (to our eyes) to be less detrimental than one might think - where the further magnification of display/print size is the rub !!

... Not to mention the fact that the pixel-pitch of monitors/displays is on the order of 10 times larger in physical size than the CoC on an 8" x 10" print. Many limitations affecting spatial-frequency resolution.

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Detail Man
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Correction: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jun 20, 2012

Detail Man wrote:

Detail Man wrote:

... the subjective sharpness of a print corresponds to the area under the MTF curve between the spatial frequencies of (0.5 x magnification) and (2 x magnification) when spatial frequency is plotted on a logarithmic scale .

... if we make an 8x10 (or 8x12) print from a 35mm negative we have to magnify the negative by a factor of 8 (since the negative is approximately 1" x 1.5"). So as far as the SQF is concerned, the area under the MTF curve of the lens between 4 and 16 cycles/mm is then what really counts .

http://www.bobatkins.com/photography/technical/mtf/mtf4.html

I am beginning to think that spatial frequency resolving abilities of human visual perception just might have a fair bit to do with why stopping-down to F-Numbers higher than 2.0 (at 700nM, with pixel-pitches on the order of 4.0 Microns on M43 image-sensors) appears (to our eyes) to be less detrimental than one might think - where the further magnification of display/print size is the rub !!

... Not to mention the fact that the pixel-pitch of monitors/displays is on the order of 10 times larger in physical size than the CoC on an 8" x 10" print. Many limitations affecting spatial-frequency resolution .

Having read bobn2 's interesting post here:

http://forums.dpreview.com/forums/read.asp?forum=1041&message=41829529

... regarding Cambridge in Color's "Diffraction Limited Aperture Estimator" here:

http://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm

... I am reminded of Bob Atkin's interesting web-page regarding the influences of the "Subjective Quality Factor" (SQF), taking into account the limitations of human visual acuity (including viewing-size and viewing-distance), as well as the profound effect of non-ideal optical lens-system aberrations on the net/actual/relevant perceptual results themselves (being the subject of debate)

See example graph at: http://www.bobatkins.com/photography/technical/mtf/mtf4.html

Further SQF information: http://www.imatest.com/docs/sqf/

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Moonlight Knight
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Re: Correction: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Jun 20, 2012

Thanks for the links. They look interesting, and seem to correlate with questions I've been searching about:

1. What is microcontrast, visually? What is Leica "Pop"?

2. What exactly are these attributes from a MTF point of view? Getting this answer, and assume that we have accurate MTF graphs for lenses, it becomes easier to find lenses with high microcontrast.

3. If I don't have those expensive lenses, how do I PP the photos to look like them?

My findings on these topics so far are as follows:

1. microcontrast = pop = making the subject jump out at you (or a visual "depth") even with a sharp background with deep DOF. Reportedly Zeiss and Leica lenses do these best?

2. lensrentals.com states that MTF-50 = resolution = microcontrast, and I suspect this may not be the right answer. In particular, lensrentals.com proved that the 20mm f/1.7 has higher resolution than the PL 25mm f/1.4, but many people here prefer the latter instead. There was a guy in Nikon forum asking about which Nikon lenses have good microcontrast and suggested that MTF-10 = microcontrast with good arguments. Reading about the SQF and the pinhole paper above, I'm inclined to believe that microcontrast is probably not MTF-50, but something like MTF-10 as suggested instead. (Unfortunately that thread does not yield definite answers for me, and mentioned only one or two Nikon lenses possibly having high microcontrast, and seems to conclude that microcontrast is not always a good thing, Nikon lenses giving more natural images than Zeiss does, and people should get Zeiss lenses if they really want microcontrast, etc.)

3. I have read two people saying that using a Photoshop unsharp mask with a large radius from 40 to 50 gives a boost to microcontrast. However, I'm still finding how to do a similar thing in Lightroom 4.1, which reportedly has a different sharpening algorithm from unsharp mask.

I'm still searching for definitive answers to all these questions. Please enlighten me.

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Detail Man
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Re: Correction: MTF and "The Sharper Image" - What matters most ?
In reply to Moonlight Knight, Jun 20, 2012

Moonlight Knight wrote:

Thanks for the links. They look interesting, and seem to correlate with questions I've been searching about:

1. What is microcontrast, visually? What is Leica "Pop"?

2. What exactly are these attributes from a MTF point of view? Getting this answer, and assume that we have accurate MTF graphs for lenses, it becomes easier to find lenses with high microcontrast.

3. If I don't have those expensive lenses, how do I PP the photos to look like them?

I'm still searching for definitive answers to all these questions. Please enlighten me.

Read all of the materials associated with all of the links that I have provided in my posts on this thread, and you will know pretty much all that I know about it. As I understand it, the term "micro-contrast" is the same thing as "contrast-sensitivity", which is (in perceptual reality, as much as there can be one in an objective sense) a complex relationship involving the composite modulation transfer function (MTF) of the entire system (from lens to viewing medium), viewing size, viewing distance and the viewer's own human visual perceptual response. So simple, eh ?

1. microcontrast = pop = making the subject jump out at you (or a visual "depth") even with a sharp background with deep DOF. Reportedly Zeiss and Leica lenses do these best?

See above for my best understanding of what the phrase describes.

2. lensrentals.com states that MTF-50 = resolution = microcontrast, and I suspect this may not be the right answer.

It's more than just where the 50% point is of the MFT response. It involves the entire composite MTF curve. Read the "Simple Minded Enginner" paper references in the original post on this thread. It addresses that to some extent.

In particular, lensrentals.com proved that the 20mm f/1.7 has higher resolution than the PL 25mm f/1.4, but many people here prefer the latter instead. There was a guy in Nikon forum asking about which Nikon lenses have good microcontrast and suggested that MTF-10 = microcontrast with good arguments. Reading about the SQF and the pinhole paper above, I'm inclined to believe that microcontrast is probably not MTF-50, but something like MTF-10 as suggested instead. (Unfortunately that thread does not yield definite answers for me, and mentioned only one or two Nikon lenses possibly having high microcontrast, and seems to conclude that microcontrast is not always a good thing, Nikon lenses giving more natural images than Zeiss does, and people should get Zeiss lenses if they really want microcontrast, etc.).

Again, "resolution" is not the same thing as "contrast-sensitivity". The meaning of the latter phrase appears to depend upon the shape of the MTF curve - largely between a sub-octave and one octave of the location on the X-axis that Bob Atkins describes on his web-page. The human Contrast Sensitivity Function (different for different viewers) is implicitly involved in this matter. Atkins understands it and explains it better than I am able. Over-simplifications likely do not suffice.

3. I have read two people saying that using a Photoshop unsharp mask with a large radius from 40 to 50 gives a boost to microcontrast. However, I'm still finding how to do a similar thing in Lightroom 4.1, which reportedly has a different sharpening algorithm from unsharp mask.

Adobe stuff is largely "secret sauce". LR 3.x/4.x and CR 6/x/7.x appear to use a combination of a USM-related process combined with a deconvolution-deblurring process. The "Detail" slider acts like a "mixer", "panning" the composition of the composite output of the Sharpening tools between all "USM-related" (when "Detail"=0) to all deconvolution-deblurring (when "Detail"=100). That much has been vaguely cionfirmed by Adobe's Eric Chan on the Luminous Landscape forum. The "Amount" control acts (in some way) as a "wet/dry" control, "panning" the composition of the composite output of the Sharpening tools between no sharpening ("original input signal" only) and full sharpening (no "original signal" in output). USM-related processes can boost the composite MTF

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Derek Bach
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Re: MTF and "The Sharper Image" - What matters most ? Thanks!
In reply to Detail Man, Jun 20, 2012

All interesting and makes a pleasant change from all the: "which handbag can I use to carry my...."
Thanks,
Derek

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, Apr 9, 2013

While the perception of image "sharpness" (contrast, micro-contrast) depends on some amount of image resolution existing, it appears to have more to do with the overall shape of the composite MTF response curve - specifically the amount of the area under the composite MTF response curve:

For a lens to be regarded as having good contrast, it will need to have high MTF-values at low line frequencies. It can already be down at zero by 50 lp/mm as long as it has high values before that. Its contrast will be perceived as high, without its resolution being good.

Source: http://www.photodo.com/imgs/articles/169/sharpenupmtfkurva3.gif

The solid curve represents a lens with high MTF at low line frequenses - a 'contrasty' lens. The dashed curve represents a high resolution lens.

http://www.photodo.com/topic_110.html

A more thorough treatment regarding this subject exists at:

http://www.bobatkins.com/photography/technical/mtf/mtf4.html

The above information (also) applies to the composite MTF response curves of cameras + lenses.

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hjulenissen
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, May 15, 2013

http://www.dpreview.com/forums/post/40405732

"UNIQUENESS OF BLUR MEASURES

After discussing usual approaches to measuring blur, we show theoretically that there is essentially a unique way to quantify blur by a single number. It is the variance of position and therefore is given by the second derivative at the origin of the Fourier transform. This somewhat surprisingly  implies that blur should be especially sensitive to attenuation of the low frequencies. This is confirmed by a seriesĀ of experiments.

http://perso.telecom-paristech.fr/~gousseau/ProjMVA/Flou/blur_long.pdf "

Is a low-contrast image ever perceived as "sharp"?

-h

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to hjulenissen, May 15, 2013

hjulenissen wrote:

http://www.dpreview.com/forums/post/40405732

"UNIQUENESS OF BLUR MEASURES

After discussing usual approaches to measuring blur, we show theoretically that there is essentially a unique way to quantify blur by a single number. It is the variance of position and therefore is given by the second derivative at the origin of the Fourier transform. This somewhat surprisingly  implies that blur should be especially sensitive to attenuation of the low frequencies. This is confirmed by a series of experiments.

http://perso.telecom-paristech.fr/~gousseau/ProjMVA/Flou/blur_long.pdf "

Thanks for the very interesting link revealing the nature of the BxU unit, as well as rather twisting (my) mind considerably. What is puzzling to me is that the "high-pass" spatial frequency response that they use is more of a notch-filter at around F=0.3 which then equals the Gaussian response at lower frequencies. That seems counter to what they are saying - that the "key" is the 2nd derivative of the Fourier transform (MTF) at zero spatial frequency ...

It's remarkable to see processing using the "brick-wall" low-pass produce "sharper" appearing results than either the Gaussian or the "high-pass" response. Plenty of interesting "food for thought" there.

Is a low-contrast image ever perceived as "sharp"?

The other interesting thing is that the CSF graphs that I can find that do reflect testing down to around 1 cycle/degree (which is not all that low, as compared to zero spatial frequency) show an around 10:1 attenuation of reported response. Thus, if it is the characteristics of the image existing near zero spatial frequency that matter so crucially regarding the perception of "blur", it seems that such characteristics occur in a region that appears to be highly attenuated where it comes to human visual perception (presumably even more than 10:1 relative to maximum response). That situation seems a bit paradoxical to me - that information so attenuated would at the same time be so crucial.

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hjulenissen
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, May 15, 2013

Its been a while since I read that paper, but could it be that the second derivative at DC just "happens to correlate" with the perceptual characteristic that we are interested in?

I.e. there could be some other, unknown, parameter that more robustly predicts "sharpness", but this measure happens to work well for the responses tested?

-h

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Detail Man
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Re: MTF and "The Sharper Image" - What matters most ?
In reply to hjulenissen, May 15, 2013

hjulenissen wrote:

Its been a while since I read that paper, but could it be that the second derivative at DC just "happens to correlate" with the perceptual characteristic that we are interested in?

That 2nd derivative is highest in value at DC in the case of the "Chinese hat" MTF response of diffraction through a circular aperture, though not as much so in the case of a Gaussian MTF response (where it increases to maximum at a somewhat higher spatial frequency). Note that it has a value of zero at DC in the case of the "brick wall" low-pass (which appears the "sharpest").

I.e. there could be some other, unknown, parameter that more robustly predicts "sharpness", but this measure happens to work well for the responses tested?

When I think about a single (unipolar) spatial domain step (the integral of an impulse, and not a periodic train of pulses or impulses), representing an image made up of half light and half dark, the Fourier transform is a distribution with a magnitude that is inversely proportional to spatial frequency:

Source: http://courses.washington.edu/matlab2/Lesson_11_12.png

The 1st and 2nd derivatives are highest at zero spatial frequency, and we know that such a transition between light and dark would appear as "sharp" to our eyes - even though the magnitude of the spatial frequency transform decreases in inverse proportion to spatial frequency.

Repeating (unipolar) spatial line-pairs centered around zero have a spatial frequency spectrum of:

( 4/pi ) * ( pi/8 + cos (2*pi*K) - 1/3 cos (6*pi*K) + 1/5 cos (10*pi*K) - 1/7 cos (14*pi*K) + ... )

where K is in units of cycles.

The highest magnitude component is at DC (1/2), and the magnitude of each of the periodically spaced components decreases in inverse proportion to spatial frequency.

Because these functions must be unipolar (positive valued only), we cannot (mathematically) remove the DC components (which explains why the high-pass filter used in the referenced paper could not have a spatial frequency magnitude response that decreases to zero at zero frequency).

We can see that both of the example spatial frequency spectrums (above) decrease with increasing spatial frequency (and thus have the highest 1st and 2nd derivatives at the lowest spatial frequencies), and we also have no doubt that they would appear "sharp" to our eyes (assuming that the spatial frequency repetition-rate in the case of the square-wave made up of line-pairs is limited to one where the human contrast sensitivity response passes enough harmonics).

DM ... P

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Detail Man
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Addendum: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, May 15, 2013

Detail Man wrote:

We can see that both of the example spatial frequency spectrums (above) decrease with increasing spatial frequency (and thus have the highest 1st and 2nd derivatives at the lowest spatial frequencies), and we also have no doubt that they would appear "sharp" to our eyes (assuming that the spatial frequency repetition-rate in the case of the square-wave made up of line-pairs is limited to one where the human contrast sensitivity response passes enough harmonics).

It seems that since the "brick wall" low-pass filtered image fared so well in the referenced paper, and if it is true that the perceived "blur" is largely determined by the 2nd derivative of the spectrum at very low spatial frequencies, then it might seem that a "brick wall" low-pass filtered square-wave made up of repeating line-pairs - where the odd harmonics of the fundamental frequency existing in the spectrum are at some spatial frequency removed entirely - (should) appear as "sharp".

Let us have a look at the output of our own ideal "brick wall" spatial low-pass filtered line-pairs:

Ideal Low-Pass Filtered Line Pairs

At the top-left is the result of removing spectral components other than the fundamental sinusoidal frequency component. We presume that this sinusoid would not appear "sharper" than a square-wave of line-pairs. At the top-right we add the 3rd harmonic to the fundamental. At the bottom-left, the 5th harmonic, as well. At the bottom-right, we have now added all harmonics through the 7th harmonic. The "ringing" behavior seen is called "Gibbs phenomena".

The referenced paper seems to assert that one of the above waveforms representing transitions of light to dark in a test-image would appear "as sharp" (or even, of all things, even "sharper") than a square-wave made up of ideal line-pairs alternating between light and dark ...

... because the higher spatial frequency components are alleged to not be highly significant in determining what looks "sharp" to our eyes - even though the rates of change of the above transitions (between dark to light, and light to dark) are lower than the ideal square-wave case.

Does that make intuitive sense to you ? It seems rather puzzling to me. Have you ever been "Blur Experienced" ? We depend upon these (BxU) units all the time when viewing DxOMark test results.

DM ...

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Moti
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Re: Addendum: MTF and "The Sharper Image" - What matters most ?
In reply to Detail Man, May 15, 2013

That is a very interesting thread. I have tried pinhole photography myself some 40 years ago but unfortunately, there was not much information available for me at that time. All I could find was an article that described the principle but wasn't very technical so there was lots of trial and error involved. Nevertheless I managed to produce some photos but they were not very good.

But I have a good friend in Brussels who does pin hole photography for many yeas and became very successful in it. All she uses is an old biscuit tin box, a piece of 4x5 film in it and a black scotch tape as a shutter. Then she goes out, almost every day, chooses a subject, removes the tape and reads a book for about 15-30 minutes hoping for the best...  Aren't we lucky with digital photography?

If you are interested to see some of her work, here's a link:

http://www.clairelatouche.be/galerie6/galerie6.htm

Cheers
Moti

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