Monday, January 27, 2020

Method for Measuring the Area of Radiometric Apertures

Method for Measuring the Area of Radiometric Apertures ERREIRA DA   Method for measuring the area of radiometric apertures using the ratio of Gaussian beams I propose and demonstrate a method for determining the area of radiometric apertures using the power ratio between Gaussian beams. The result relies on measuring the power of an optical beam of known radius with and without the radiometric aperture. The impact of the characterization of the laser beam and of the radiometric measurements on the area estimation is discussed and a 3-mm in-diameter sample is measured for validation. The contactless method is fast and simple and results in a relative uncertainty of 0.12%.   Calibration of the area of an aperture is necessary for radiometric and photometric measurements, including spectral irradiance [1- 4] and the realization of the SI unit candela [5-7]. The plethora of methods reported in literature can be assorted whether they are contact or contactless. Contact methods include probing the aperture border with an stylus, which position is mapped by an interferometric system [8]. Contactless methods are preferable as the possibility of damaging the sharp edge of the aperture during the measurement is avoided. A camera with an objective lens can be used for taking digital pictures of parts of the inner perimeter of the aperture, while an interferometric system is used for measuring the displacement of the images, allowing them to be further stithed together [9]. Another approach consists in raster scanning the aperture relative to a laser focused in a small spot in the aperture plane to determine the diameter at some radial angles [10]. Methods based on radiometric ratios have also been reported and depend on comparing measurements performed with a light overfilled aperture and a reference value. A spatially-uniform beam emerging from an integrating sphere can be used to compare the radiometric values obtained with the aperture under calibration and with the reference one [11]. Similarly a matrix of small-spot laser sources can be used [12, 13], with the reference provided by the known uniform irradiance distribution. In this paper I propose a method for determining the area of a radiometric aperture using the ratio between Gaussian laser beams. The result is obtained from measurements of the optical power transmitted through the overfilled aperture compared to the total optical power without the aperture, with the beam radius at the aperture plane previously characterized. The technique is contactless and the measurement is relatively fast, providing an alternative way for measuring radiometric apertures. A. Model The method proposed for determining the area of the aperture is based on measuring the radiometric ratio between the beam limited by the aperture and the full beam. Consider a Gaussian beam propagating along the zˆ  axis with an intensity distribution in the radial direction à Ã‚  on the transversal plane described as I (1) where the beam radius à Ã¢â‚¬ ° (z) is [14] (2) and the waist radius is à Ã¢â‚¬ °0 = à Ã¢â‚¬ ° (0). The beam radii in the analysis are taken at 1/e2 of the maximum intensity. The total optical power of the beam is obtained by integrating its intensity over the transversal area as   Ã‚   Ptotal /2(3) The circular radiometric aperture is modelled as a Boxcar function with mean radius r à Ã¢â‚¬ ° (z) and transmittance given by g (x, y) = rect(4) Positioning the aperture in the plane orthogonal to the beam axis at à Ã‚ =0 reduces the measured optical power in eq. (3) to Z r Pap (z) =I (à Ã‚ , z) 2à Ã¢â€š ¬Ãƒ Ã‚ dà Ã‚ (5) 0 The ratio between the optical power limited by the aperture at position z and the total optical power of the beam is thus [14] (z)2r2 R(6) The radius of the aperture is obtained by inverting eq. (6), resulting in r (7) Equation (7) reveals the dependence of the aperture radius on the beam radius à Ã¢â‚¬ ° and radiometric ratio R measured at a given axial position. The sensitivity coefficients of the radius equation relative to those components are 2(8) (z) The uncertainty of the measured area is composed [15] as ur (9) The area of the radiometric aperture is then trivially obtained from the circle formula, S = à Ã¢â€š ¬r2, with uncertainty given by uS = 2à Ã¢â€š ¬rur. B. Method The first step of the method is the determination of the longitudinal profile of the Gaussian beam. This can be accomplished in practice by using the knife-edge scanning method [16] or using a spatially-resolving photodetector (for example, a CMOS or CCD camera). While the later can be troubling for beams wider than the sensitive area of the camera, the primer requires caution relative to radial asymmetries in the beam profile. The astigmatism of the beam must be verified by knife-edge scanning along orthogonal directions in the transversal plane and the mean radius is considered. The beam longitudinal profile reveals important information about the tolerance of the axial positioning of the aperture relative to the transversal plane where the beam is determined. Next step consists on positioning the aperture in the beam path. Carefully placing the aperture front plane at the axial position where the beam has been characterized avoids the need for a correction on the beam radius value. The aperture under measurement must then be centralized relative to the beam axis. A recursive gradient search can be performed along the plane axes until convergence at the maximum optical power, where à Ã‚ Ãƒ ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 0. The value of the optical power measured with the aperture is compared to the total optical power measured without it. This ratio and the mean beam radius are substituted in eq. (7) and the aperture radius is determined. Research Article Applied Optics 2 A laser diode with continuous-wave emission at 633 nm is collected with an objective lens into a meter-long single-mode optical fiber (Thorlabs SM600 [17]), which acts as a spatial filter by selecting the LP01 transversal mode. The beam is launched into free-space through the tip of an FC-PC connector and collimated using an 1-large AR-coated plano-convex lens (L2) with a focal length of 38.2 mm, as illustrated in Fig. 1. A similar lens (L3) with 150-mm long focal length focuses the beam into the photo-detector. Fig. 1. Experimental setup. LD: laser diode; L: plano-convex lens; C: fiber connector; PD: photo-detector; PC: personal computer. The beam profile is determined using the knife-edge method. A pair of razor blades is scanned in the plane orthogonal to the optical beam in both xˆ  (horizontal) and yˆ  (vertical) directions, using a pair of linear actuators (Newport TRA25PPD and CMA25PP). The optical power is measured by an optical power meter with a diffuser probe (Thorlabs PM100). Data acquisition and transversal positioning of the knives and aperture are performed with a personal computer. Flip mounts allow for selecting either the knives or the aperture, which are placed in the same xˆ  à ¢Ã‹â€ Ã¢â‚¬â„¢ yˆ  translation stage. The translation stages, the lens L3 and the photo-detector are fixed into a platform and move together to the desired position in axial direction zˆ . The aperture under characterization has nominal diameter of 3 mm and is built in anodized aluminium with sharp edges. The offset distance between the planes of the knives and the aperture is set within 0.05 mm using a multi-probe optical reflectometer [18]. An automated routine is used to position the aperture in the transversal plane relative to the optical beam by scanning it along xˆ  and yˆ  directions until it is centralized. The radiometric ratio is obtained by removing and reinserting the aperture using the flip mount while the power is measured using a silicon photodiode (Hamamatsu S1227-1010BQ) in photovoltaic mode. Calibrated trans-impedance amplifier (LabKinetics Vinculum) and digital voltmeter (Agilent 34401A) are used. Conditioning the signals for using a single range of these devices avoids linearity issues. The detector typical linearity is better than 10à ¢Ã‹â€ Ã¢â‚¬â„¢5 [19]. A. Beam width The width of the Gaussian beam is determined at different positions along the axial direction in both horizontal and vertical axes. Figure 2 shows a sample of the transversal beam profile Fig. 2. Sample of the transversal intensity profile of the beam. The slices in the details cross the center and are Gaussian fit. The longitudinal profile of the beam is evaluated by applying the knife-edge analysis at different axial positions. The optical power measured as a function of the knife position in xˆ  direction is modelled as the integral of the Gaussian intensity, resulting in the error function: P (10) Equation (10) indicates that the measured power profile reveals the horizontal beam radius à Ã¢â‚¬ °x (z). The procedure performed along the yˆ  direction returns a similar result as a function of the vertical beam radius à Ã¢â‚¬ °y (z). Figures 3a and 3b show the power measured with the knifeedge method along both xˆ  and yˆ  directions, respectively. A group of 10 scans, with 0.25-mm steps, is taken at a given axial position. Data is interpolated to steps of 0.1 mm using piecewise cubic Hermite interpolating polynomials [20]. Non-linear curve fit (Levemberg-Marquadt method) is globally applied to data with the beam radius parameter shared by all curves in the group. The beam radius values as a function of the axial distance to the collimating lens are shown in Fig. 3c. Observe that the beam profile behaves linearly at the sampled axial positions. Fitting data with eq. (2) reveals the horizontal and vertical waists localized at about 3.3 m and 3.7 m, respectively. The slope of 10à ¢Ã‹â€ Ã¢â‚¬â„¢4 indicates that a positioning error between the knives and the aperture of 0.05 mm has negligible impact on estimated radius. The beam is slightly astigmatic (horizontal radius about 1% greater than the vertical one), so the average radius is computed from both horizontal and vertical radii as /2(11) B. Radiometric ratio The radiometric ratio is determined from five groups of measurement of the total beam power, alternated with four measurements of the power limited by the aperture. Interleaved measurements allows for data interpolation and avoids slow drift effects. Each measurement is composed by a group of 30 data points, corrected by the dark measurement. Three measurement were performed at each axial position. The calibration data of the trans-impedance amplifier and voltmeter are used for correction and considered in the uncertainty budget see next section. The average ratio of 0.3373 allows for performing both measurements (with and without the aperture) in the same scale of the amplifier and voltmeter. Keeping the measurement range of the equipment fixed avoids linearity issues, which must otherwise be corrected and could burden on the uncertainty budged. C. Aperture radius/area and uncertainty budget The aperture radius is computed from the measured values of à Ã¢â‚¬ ° (z) and R (z) using eq. (7). The result obtained at three different axial distances from the collimating lens are presented in Fig. 4a. The uncertainty budget for the radius measurement is presented in Table 1. The uncertainty of the beam width and power ratio are combined with the reproducibility of the measurement. The radius measurement is obtained from the global fit of the knife-edge scan measurements. The impact of the beam divergence is obtained by multiplying this value by the maximum axial offset between the knife-edge and the aperture plane. The beam width uncertainty is dominant over all other components. Improvements over this estimation would greatly benefit the final uncertainty. The repeatability comes from the statistics of the ratio measurements. Stability of the laser source is the major component and could be iproved using a further power stabilization closedloop. The amplifier and voltmeter uncertainties are obtained Fig. 4. Experimental results: (a) aperture radius measurements and (b) its final area. The reference values are certified results. Standard uncertainties represent k=1. Table 1. Uncertainty budget for the measurement of the aperture radius (relative values). Component Type Uncertainty (k=1) Radius measurements B 5.3 ÃÆ'- 10à ¢Ã‹â€ Ã¢â‚¬â„¢4 Beam divergence [mm] B 2.3 ÃÆ'- 10à ¢Ã‹â€ Ã¢â‚¬â„¢5 Trans-impedance amplifier B 6.3 ÃÆ'- 10à ¢Ã‹â€ Ã¢â‚¬â„¢5 Voltmeter B 5.5 ÃÆ'- 10à ¢Ã‹â€ Ã¢â‚¬â„¢5 Photodiode linearity B 6.2 ÃÆ'- 10à ¢Ã‹â€ Ã¢â‚¬â„¢6 Power ratio 0.00017 Reproducibility [mm] A 0.00027 Aperture radius [mm] 0.00062 from their calibration uncertainty and from the linear regression over the measurement range. The photo-diode linearity is taken from literature. The reproducibility is taken from the independent repetitions. Among other factors, it accounts for small room temperature variation (oC), different axial positions, and repositioning of the aperture center relative to the beam axis. The final relative uncertainty obtained for the measurement of area is 0.12%. The validation of the method is assessed by comparing the results to a certified value, as shown in Table 2. The certificates present a relative uncertainty (k=1) of 0.0065 mm2 for the area value and a calibration drift (rectangular distribution) between bi-annual measurements of 0.0410 mm2 is observed, composing a combined uncertainty of 0.415 mm2. Research Article Applied Optics 4 Table 2. Experimental results and validation (k=1). Measured area Certified Relative Normalized [mm2] area [mm2] difference [%] error 7.0056  ± 0.0087 6.998  ± 0.042 0.11 0.18 The relative error between the measured and certificated values is 0.11%, while the normalized error [15] is below unit, indicating the compatibility of the results. The coverage factor of the measurements, calculated for a confidence interval of 95.45%, is k=2. The area of an aperture impacts directly on the determination of some radiometric and photometric quantities. This paper presents a simple and fast contactless method for characterizing an aperture area through the measurement of radiometric ratio of characterized Gaussian beams. The model is presented and the measurement uncertainty budget is discussed. The results are validated and indicate the method as suitable for metrology applications. References       M. White, N. P. Fox, V. E. Ralph, and N. J. Harrison, The characterization of a high-temperature black body as the basis for the NPL spectralirradiance scale, Metrologia 32, 431-434 (1995/96). P. Sperfeld, K.-H. Raatz, B. Nawo, W. Mà ¶ller, and J. Metzdorf, Spectralirradiance scale based on radiometric black-body temperature measurements, Metrologia 32, 435-439 (1995/96). P. Kà ¤rhà ¤, P. Toivanen, F. Manoochehri, and E. Ikonen, Development of a detector-based absolute spectral irradiance scale in the 380-900-nm spectral range, App. Opt. 36, 8909-8918 (1997). H. W. Yoon, C. E. Gibson, and P. Y. Barnes, Realization of the National Institute of Standards and Technology detector-based spectral irradiance scale, App. Opt. 41, 5879-5890 (2002). L. P. Boivin, A. A. Gaertner, and D. S. Gignac, Realization of the New Candela (1979) at NRC, Metrologia 24, 139-152 (1987). T. M. Goodman and P. J. Key, The NPL Radiometric Realization of the Candela, Metrologia 25, 29-40 (1988). E. Ikonen, P. Kà ¤rhà ¤, A. Lassila, F. Manoochehri, H. Fagerlund and L. Liedquist, Radiometric realization of the candela with a trap detector, Metrologia 32, 689-692 (1995/96). J. E. Martin, N. P. Fox, N. J. Harrison, B. Shipp, and M. Anklin, Determination and comparisons of aperture areas using geometric and radiometric techniques, Metrologia 35, 461-464 (1998). J. Fowler and M. Litorja, Geometric area measurements of circular apertures for radiometry at NIST, Metrologia 40, S9-S12 (2003). J. Fischer and M. Stock, A non-contact measurement of radiometric apertures with an optical microtopography sensor, Meas. Sci. Technol. 3, 693698 (1992). V. E. Anderson, N. P. Fox, and D. H. Nettleton, Highly stable, monochromatic and tunable optical radiation source and its application to high accuracy spectrophotometry, App. Opt. 31, 536-545 (1992). A. Lassila, P. Toivanen and E. Ikonen, An optical method for direct determination of the radiometric aperture area at high accuracy, Meas. Sci. Technol. 8, 973977 (1997). E. Ikonen, P. Toivanen and A. Lassila, A new optical method for high-accuracy determination of aperture area, Metrologia 35, 369-372 (1998). B. E. A. Saleh and M. C. Teich, Fundamentals of photonics, 2nd ed., 2007. JCGM 100:2008, Evaluation of measurement data Guide to the expression of uncertainty in measurement, 1st ed., 2010. M. A. C. Araà ºjo, R. Silva, E. Lima, D. P. Pereira, and P. C. de Oliveira, Measurement of Gaussian laser beam radius using the knife-edge technique: improvement on data analysis, App. Opt. 48, 393-396 (2009). Some equipment and components are cited for the sake of clarity and this does not mean endorsement or recommendation. T. Ferreira da Silva, Multi-probe remote differential optical lowcoherence reflectometer, Microw. Opt. Technol. Lett. 58, 2606-2609 (2016). A. Haapalinna, T. Kà ¼barsepp, P. Kà ¤rhà ¤, and E. Ikonen, Measurement of the absolute linearity of photodetectors with a diode laser, Meas. Sci. Technol. 10, 1075-1078 (1999). https://www.mathworks.com/help/matlab/ref/pchip.html (accessed in 10/24/2016).

Sunday, January 19, 2020

Heidi Roizen/ Building a Network Essay

In my opinion Heidi Roizen’s network is one of her greatest assets. â€Å"While other people use networks to build their business, Heidi’s business is networking. She’s very effective and uses her network to add real value.†, Randy Komisar commented on the article. Her networking skills are extremely efficient. She is really good at blending her professional with her personal networking. She always grabs the nucleus people of a network and then keeps in touch with all the people in that network. And another strength that makes Roizen’s networking successful is that she understands and pays more attention on the win-win relationship which is a core factor that differentiated her skills from others. Her style includes an unpretentious, down- to-earth, and positive personality which played an important role for her success. Additionally, as mentioned on the article by Royal Farros â€Å"Heidi is a pro at turning a brief conversation into one of substance, by contributing one or two unique ideas in a short period of time. That helps make the conversation memorable.† The downside of Roisen’s networking is that they are thousands of people that know her and in some cases people may feel they have a relationship with her, and therefore request her time for meetings. There are also some weaknesses in her networking. Her networking lacks more diversity. According to the article, she always invites the people to her party that have known half of any other people attend the party. That could potentially lead to a result that she can meet less people at one time, she could miss some important talents and opportunities. Also her networking really focuses on companies and people mostly bases in the Silicon Valley. In order to build her networking, Roizen has taken several steps. She begun building relationship with members of the press and she also attended several industry conferences and events. Later on she also decided to join the board of the Software Publishers Association (SPA). The article also mentioned that she gets motivation to get to know good-quality and talented people and be friends with then. She also knows that she is placing a bet by investing so much time in these people, but many of her bets paid off for her in the past. Additionally, she acknowledges that is easier to meet people when they are not famous, and off course it would be easier for her when they become famous because she would already have a relationship with them. And she spends a long-term effort on performance and consistency during and after each interaction to maintain a better and long living network. I think Heide should diversify more her network and try to create strong connections with leaders from other industries a besides technology and venture capital. Also because of the breath and depth of her network, she will constantly have people reaching out for her, so in my opinion she will have to be more selective of her time and people who she will interact with, and most important she will have to say no to some people. Additionally, she should probably balance more her life and reduce the number of industry events or gatherings hosted by her, which according to the article she already initiated this process. I would like to reinforce my arguments in this paragraph with something that Roizen mentioned in a news article, â€Å"At the close of my life, I’d like to look back and know that I got — and delivered — good value out of living. I’d like to know that I took advantage of the opportunities that I was blessed with for myself and my family. I want to know that I created good balance in my life, enjoyed it, lived well and enhanced the lives of others in the process.†

Saturday, January 11, 2020

John Clare Essay

John Clare (1793-1864) was born on July 13 at Helpstone, a village in Northamptonshire, close to the Lincolnshire fens. His father, Parker Clare, worked as a farm laborer. In his spare time his father was also a rustic wrestler and ballad singer. Clare attended a dame school in his native village, and then went to Glinton School in the next village. When his father became ill with rheumatism, Clare began work first as a horse-boy, then ploughboy, then as a gardener at Burghley House. In 1812 he enlisted in the militia, returning home eighteen months later. He met Martha Turner in Casterton, who joined the Clare family just before the birth of the first of their eight children. Clare’s first book of poems appeared in 1820, published by Hessey and Taylor. The volume ran to four editions in the first year, and he became celebrated in London literary society as the â€Å"peasant poet†. In 1837 Clare was admitted into Mathew Allen’s private asylum of High Beech in Epping Forest, where he stayed for four years until he discharged himself, walking the eighty miles home to Northborough in three days, eating grass on the way. He wrote two long, suffering poems, Don Juan and Child Harold, which documented his precious mental state. He was certified insane by two doctors in December 18841 and was admitted to St, Andrews County Lunatic Asylum in Northampton, where he was treated well and continued to write, producing many short, semi-mystical poems. John Clare later passed away in the institution in 1864 at the age of 71. First Love I ne’er was struck before that hour With love so sudden and so sweet, Her face it bloomed like a sweet flower And stole my heart away complete. My face turned pale as deadly pale. My legs refused to walk away, And when she looked, what could I ail? My life and all seemed turned to clay. And then my blood rushed to my face And took my eyesight quite away, The trees and bushes round the place Seemed midnight at noonday. I could not see a single thing, Words from my eyes did start — They spoke as chords do from the string, And blood burnt round my heart. Are flowers the winter’s choice? Is love’s bed always snow? She seemed to hear my silent voice, Not love’s appeals to know. I never saw so sweet a face As that I stood before. My heart has left its dwelling-place And can return no more First love is a poem, which shows the experience the poet has falling in love for the first time. It is rejoicing the love he attained for a woman named Mary Joyce however there is sadness and a feeling of dissatisfaction hovering in the background. This feeling exists, as the love was unrequited. The poem has an underlying tone of innocence and flurry of emotions as it is the poets very first attempt at love exhibiting his feelings for Mary. The opening of the first stanza only shows how sudden and unexpected the feeling was as he was never â€Å"struck before that hour†, this is followed my sibilance alliteration so sudden and so sweet further emphasizing on the shock and bewilderment of the overwhelming feeling confirming it is a new experience. He uses his heart as a symbol that she has stolen completely away however unknowingly. The paragraph continues to describe how he physically felt ill as his face turned pale a deadly pale. Generally when a person falls in love the instinct is that the blood rushed to the face, which occurs as a latter reaction. This could be because he probably already sensed that the love could not be returned as he didn’t say anything to her instead he hoped that his eyes would convey the message â€Å"words from my eyes did start†. He never came close to even touching or  talking to her however the line â€Å"all seemed to turn to clay† conveys the strong affection he attained for her. He also shows how the woman is in control of their relationship as she could mould and re-mould him as per her wish. In the second stanza he goes on to describe more of his emotions brought forward by this interaction. He makes it quite visual for us of how the love has its affect on him and how he flushes with embarrassment so much that for a moment he feels blind. The physical impact of love relates the experience of love and loss.

Thursday, January 2, 2020

Technology And Its Effects On Children - 1733 Words

Unplug Electronics With a flip of a switch or press of a button, Parents can have their child entertained for hours on end. Televisions and Tablets are the twenty-first century babysitters. The average child spends an astounding 7.5 hours per day on some form of technology (Rowan 2), when the recommend allotted amount of time should be no more than two hours (Kaneshiro 1). Technology is rapidly evolving, making limitless possibilities available for entertainment. This virtual â€Å"babysitter† enables the parents to devote all their time and effort into their work or engross in technology with limited amounts of distraction from the children. Although, the parents are able to have free time, excessive amounts of screen time is proven to be detrimental to their child’s health and overall well-being. The technology that is drastically making life easier is a big blessing, but at the same time is a big curse. Twelve percent of all children in America are consider to be ove rweight or obese (Kushi, ETAL 1). Many factors contribute to obese children, but one major similarity in obese children is the excessive amounts screen time. Watching television and playing video games encourage many unhealthy habit that contribute to weight gain. The act of watching television teaches the unhealthy habit of long periods without physical activity, increased snacking behavior, and interferes with normal sleeping patterns (Strasburger 1) Apart from sleeping, children spend most of their timeShow MoreRelatedTechnology And Its Effect On Children981 Words   |  4 PagesPresent day technology today has helped us connect with others miles away through E-mail, Facebook, Twitter, YouTube and other forms of social media. 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