The success of nonlinear optics relies largely on pulse-to-pulse consistency. In contrast, covariance-based techniques used in photoionization electron spectroscopy and mass spectrometry have shown that a wealth of information can be extracted from noise that is lost when averaging multiple measurements. Here, we apply covariance-based detection to nonlinear optical spectroscopy, and show that noise in a femtosecond laser is not necessarily a liability to be mitigated, but can act as a unique and powerful asset. As a proof of principle we apply this approach to the process of stimulated Raman scattering in α-quartz. Our results demonstrate how nonlinear processes in the sample can encode correlations between the spectral components of ultrashort pulses with uncorrelated stochastic fluctuations. This in turn provides richer information compared with the standard nonlinear optics techniques that are based on averages over many repetitions with well-behaved laser pulses. These proof-of-principle results suggest that covariance-based nonlinear spectroscopy will improve the applicability of fs nonlinear spectroscopy in wavelength ranges where stable, transform-limited pulses are not available, such as X-ray free-electron lasers which naturally have spectrally noisy pulses ideally suited for this approach.

Background

BoneTour is a campaign conducted throughout the Italian territory for the assessment of Italian people bone status and for the prevention of osteoporosis.

Methods

A total of 7305 sequential subjects of both sexes were screened, collecting clinical data through the FRAX™ questionnaire, and measuring heel bone stiffness by Quantitative Ultrasonography (QUS). The 10-year risk for hip and major osteoporotic fractures was calculated taking into account personal or family history of fragility fracture, smoking, alcohol abuse, rheumatoid arthritis, prolonged steroids assumption. Additional risk factors were evaluated, including early menopause, poor sunlight exposure, low dietary calcium intake, physical inactivity, number of pregnancies, months of lactation, tobacco cigarettes smoked per year, specific causes of secondary osteoporosis. Through a correlation study, the influence of each factor on the development of osteoporosis was analyzed.

Results

As many as 18 % of women suffer from osteoporosis, as defined by QUS T-score. The calculation of FRAX™ confirmed the weight of the already known risk factors. The correlation study revealed the significance of some additional factors, such as hyperthyroidism, nephrolithiasis, Crohn disease, ulcerative colitis, celiac disease, poor sun exposure, and oophorectomy before age 50.

Conclusions

The high prevalence of secondary osteoporosis in the Italian population clearly indicates the importance of additional risk factors not yet included in the FRAX™ algorithm, for which preventive measures should be considered. Screening campaigns may allow both early diagnosis and access to treatment.